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introduction what would it be like to live in a one-room cabin ? well , things would probably be pretty simple . you would eat , sleep , work , and relax in a single room—which might be a bit cramped , but would certainly make cleaning the house a snap ! prokaryotic cells , the simple cells of organisms like bacteria ,...
prokaryotic vs. eukaryotic cells what are the key features of eukaryotic cells ? unlike prokaryotic cells , eukaryotic cells have : a membrane-bound nucleus , a central cavity surrounded by membrane that houses the cell ’ s genetic material . a number of membrane-bound organelles , compartments with specialized functio...
what exactly does a central vacuole do ?
introduction what would it be like to live in a one-room cabin ? well , things would probably be pretty simple . you would eat , sleep , work , and relax in a single room—which might be a bit cramped , but would certainly make cleaning the house a snap ! prokaryotic cells , the simple cells of organisms like bacteria ,...
introduction what would it be like to live in a one-room cabin ? well , things would probably be pretty simple .
what is funecation of centriole ?
introduction what would it be like to live in a one-room cabin ? well , things would probably be pretty simple . you would eat , sleep , work , and relax in a single room—which might be a bit cramped , but would certainly make cleaning the house a snap ! prokaryotic cells , the simple cells of organisms like bacteria ,...
in fact , it ’ s a big part of the reason why eukaryotic cells can grow to be many times larger than prokaryotic ones . prokaryotic vs. eukaryotic cells what are the key features of eukaryotic cells ? unlike prokaryotic cells , eukaryotic cells have : a membrane-bound nucleus , a central cavity surrounded by membrane t...
what holds eukaryotic cells of an organism together as tissues ?
introduction what would it be like to live in a one-room cabin ? well , things would probably be pretty simple . you would eat , sleep , work , and relax in a single room—which might be a bit cramped , but would certainly make cleaning the house a snap ! prokaryotic cells , the simple cells of organisms like bacteria ,...
for instance , compartments called lysosomes , which act as recycling centers for the cell , must maintain an acidic ph in order to dispose of cellular waste . similarly , structures called peroxisomes carry out chemical reactions called oxidation reactions and produce hydrogen peroxide , both of which would damage the...
are there chemical bonds between them ?
introduction what would it be like to live in a one-room cabin ? well , things would probably be pretty simple . you would eat , sleep , work , and relax in a single room—which might be a bit cramped , but would certainly make cleaning the house a snap ! prokaryotic cells , the simple cells of organisms like bacteria ,...
already know what part of the cell you want to visit ? use the list below to jump to your region of interest : plasma membrane and cytoplasm nucleus and ribosomes endomembrane system mitochondria , chloroplasts , and peroxisomes cytoskeleton extracellular matrix and cell wall cell junctions diagram of a typical animal ...
in the diagram of the typical animal cell , what is cytosol ?
introduction what would it be like to live in a one-room cabin ? well , things would probably be pretty simple . you would eat , sleep , work , and relax in a single room—which might be a bit cramped , but would certainly make cleaning the house a snap ! prokaryotic cells , the simple cells of organisms like bacteria ,...
introduction what would it be like to live in a one-room cabin ? well , things would probably be pretty simple .
what kingdoms do eukaryotes belong to ?
what is multiple sclerosis ? sometimes , your body ’ s defense system can go rogue . like double agents your immune cells can turn and start causing damage to organs or tissues within your own system . one of the tactics used by these delinquent cells is to cut communications between your brain ( hq ) and your organs ,...
in addition , the risk for this disease decreases for people who immigrate from countries further from the equator to countries that are closer to the equator . as countries far from the equator have less sunshine , the people living there tend to have lower levels of vitamin d , leading to the hypothesis that the lack...
what is the efficacy of vitamin d supplements versus naturally created vitamin d with exposure to sunlight ?
hi , i 'm tom heinan ! what do you work on ? i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their heal...
what do you do when you ’ re not programming ? i code a lot at work , and i also code a lot for fun , but when i ’ m not writing code , i like to spend time outside . camping and hiking are always a good time , and we ’ ve got plenty of great places to do so here in california .
and as a question , how can i turn that code into an operating system like we make an application software using the code ?
hi , i 'm tom heinan ! what do you work on ? i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their heal...
i also do a bit of back-end code in ruby , developing the apis that our app needs in order to communicate health data securely and reliably . our patients use the mobile app to schedule appointments , get virtual triage for common issues , and communicate with their doctors , so i try my best to squash bugs and improve...
what exactly are `` bugs '' ?
hi , i 'm tom heinan ! what do you work on ? i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their heal...
i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their health and wellness effectively . i also do a bit of back-end code in ruby , developing the apis that our app needs in order to communicate health...
what the heck is ruby ?
hi , i 'm tom heinan ! what do you work on ? i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their heal...
i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their health and wellness effectively . i also do a bit...
how many bugs have you squashed in the app ?
hi , i 'm tom heinan ! what do you work on ? i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their heal...
my parents bought our first family computer in 1986 , the year i was born . it was an apple iigs , and i started playing around with gs/os as soon as i could read . i learned basic html and javascript in elementary school ( i even got the computers merit badge in boy scouts ! )
how old is the apple iggs ?
hi , i 'm tom heinan ! what do you work on ? i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their heal...
i love acting , and i was a member of my university ’ s improv comedy team for several years - we still have the occasional nerd reunion in nova scotia , where i went to school . being a software engineer doesn ’ t give you a whole lot of extra time for theatrics , but if you ’ ve watched amc ’ s the walking dead , you...
is lee in the walking dead ?
hi , i 'm tom heinan ! what do you work on ? i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their heal...
when i got to university , i skipped over many of the more traditional language courses ( bash scripting , c++ ) and instead taught myself the basics of ruby , which remains one of my favourite languages today . for me , the hardest thing about learning any language is finding a good place to start . taking a hundred p...
what is the hardest programming language in the world ?
hi , i 'm tom heinan ! what do you work on ? i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their heal...
hi , i 'm tom heinan ! what do you work on ?
have you ever provisioned a polycom voip phone ?
hi , i 'm tom heinan ! what do you work on ? i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their heal...
i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their health and wellness effectively . i also do a bit...
how do you manage to be a dead dude on twd ?
hi , i 'm tom heinan ! what do you work on ? i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their heal...
i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their health and wellness effectively . i also do a bit...
how to develop a dictionary app ?
hi , i 'm tom heinan ! what do you work on ? i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their heal...
what ’ s your one piece of advice for new programmers ? find a language you love , make cool stuff with it , and never be afraid to experiment .
how do you make your apps ?
hi , i 'm tom heinan ! what do you work on ? i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their heal...
and then took ap computer science in high school , the curriculum for which was mostly introductory java . when i got to university , i skipped over many of the more traditional language courses ( bash scripting , c++ ) and instead taught myself the basics of ruby , which remains one of my favourite languages today . f...
what is bash scripting and c++ ?
hi , i 'm tom heinan ! what do you work on ? i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their heal...
what do you work on ? i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their health and wellness effecti...
does your medical app also involve scheduling for dentists and periodontists ?
hi , i 'm tom heinan ! what do you work on ? i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their heal...
it was an apple iigs , and i started playing around with gs/os as soon as i could read . i learned basic html and javascript in elementary school ( i even got the computers merit badge in boy scouts ! ) and then took ap computer science in high school , the curriculum for which was mostly introductory java . when i got...
also , what is the difference between javascript and java ?
hi , i 'm tom heinan ! what do you work on ? i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their heal...
hi , i 'm tom heinan ! what do you work on ?
what is hard disk and dc rom ?
hi , i 'm tom heinan ! what do you work on ? i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their heal...
i work for a company called one medical group , which is a technology-enabled medical practice . i spend most of my time working on our mobile app in objective-c , where we ’ re implementing all sorts of cutting edge product features aimed at helping people manage their health and wellness effectively . i also do a bit...
can people call for an emergency vehicle with the app ?
when we calculate probabilities involving one event and another event occurring , we multiply their probabilities . in some cases , the first event happening impacts the probability of the second event . we call these dependent events . in other cases , the first event happening does not impact the probability of the s...
in some cases , the first event happening impacts the probability of the second event . we call these dependent events . in other cases , the first event happening does not impact the probability of the seconds .
how does the general multiplication rule apply to three events ?
background stokes ' theorem line integrals flux in 3d curl the formula ( quick review ) stokes ' theorem is a tool to turn the surface integral of a curl vector field into a line integral around the boundary of that surface , or vice versa . specifically , here 's what it says : $ \displaystyle \overbrace { \underbrace...
luckily for us , this particular function is one of the special ones that do . $ \bluee { \textbf { f } } = \left [ \begin { array } { c } y^2 \ z^2 \ x^2 \end { array } \right ] $ concept check : find a vector field $ \textbf { g } ( x , y , z ) $ satisfying the property $ \nabla \times \textbf { g } = \bluee { \textb...
how is the gradient of g equal to f in the second example ?
what you should be familiar with before taking this lesson a matrix is a rectangular arrangement of numbers into rows and columns . the dimensions of a matrix tell the number of rows and columns of the matrix in that order . since matrix $ a $ has $ 2 $ rows and $ 3 $ columns , it is called a $ 2\times 3 $ matrix . if ...
if this is new to you , we recommend that you check out our intro to matrices . in matrix multiplication , each entry in the product matrix is the dot product of a row in the first matrix and and a column in the second matrix . if this is new to you , we recommend that you check out our matrix multiplication article .
how do you find the multiplicative inverse of a matrix ?
what you should be familiar with before taking this lesson a matrix is a rectangular arrangement of numbers into rows and columns . the dimensions of a matrix tell the number of rows and columns of the matrix in that order . since matrix $ a $ has $ 2 $ rows and $ 3 $ columns , it is called a $ 2\times 3 $ matrix . if ...
if this is new to you , we recommend that you check out our matrix multiplication article . definition of identity matrix the $ n\times n $ identity matrix , denoted $ i_n $ , is a matrix with $ n $ rows and $ n $ columns . the entries on the diagonal from the upper left to the bottom right are all $ 1 $ 's , and all o...
how do you find the identity matrix for a matrix that is not n by n ?
what you should be familiar with before taking this lesson a matrix is a rectangular arrangement of numbers into rows and columns . the dimensions of a matrix tell the number of rows and columns of the matrix in that order . since matrix $ a $ has $ 2 $ rows and $ 3 $ columns , it is called a $ 2\times 3 $ matrix . if ...
if this is new to you , we recommend that you check out our intro to matrices . in matrix multiplication , each entry in the product matrix is the dot product of a row in the first matrix and and a column in the second matrix . if this is new to you , we recommend that you check out our matrix multiplication article .
can anyone give an example of a matrix without a multiplicative inverse ?
what you should be familiar with before taking this lesson a matrix is a rectangular arrangement of numbers into rows and columns . the dimensions of a matrix tell the number of rows and columns of the matrix in that order . since matrix $ a $ has $ 2 $ rows and $ 3 $ columns , it is called a $ 2\times 3 $ matrix . if ...
connections to the real numbers multiplicative identities the identity matrix $ i $ plays a similar role to what the number $ 1 $ plays in the real number system . the number $ 1 $ |the identity matrix $ i $ - | - | - the product of $ 1 $ and any number $ a $ is $ a $ . $ ( a\cdot 1=1\cdot a=a ) $ | the product of a ma...
can we have i matrix with dimensions 1*1 ?
what you should be familiar with before taking this lesson a matrix is a rectangular arrangement of numbers into rows and columns . the dimensions of a matrix tell the number of rows and columns of the matrix in that order . since matrix $ a $ has $ 2 $ rows and $ 3 $ columns , it is called a $ 2\times 3 $ matrix . if ...
if this is new to you , we recommend that you check out our matrix multiplication article . definition of identity matrix the $ n\times n $ identity matrix , denoted $ i_n $ , is a matrix with $ n $ rows and $ n $ columns . the entries on the diagonal from the upper left to the bottom right are all $ 1 $ 's , and all o...
could you have multiplicative inverses on two matrices that have different dimensions i.e a 2x3 matrix multiplied a 3x2 matrix that results in the identity matrix ?
what you should be familiar with before taking this lesson a matrix is a rectangular arrangement of numbers into rows and columns . the dimensions of a matrix tell the number of rows and columns of the matrix in that order . since matrix $ a $ has $ 2 $ rows and $ 3 $ columns , it is called a $ 2\times 3 $ matrix . if ...
$ ( a\cdot 1=1\cdot a=a ) $ | the product of a matrix $ a $ and the appropriate identity matrix $ i $ is $ a $ . $ ( a\cdot i=i\cdot a=a ) $ multiplicative inverses two real numbers whose product is the multiplicative identity are called multiplicative inverses . for example , the numbers $ \dfrac13 $ and $ 3 $ are mul...
can you define multiplicative inverses ?
have you ever wondered why some people need glasses and others don ’ t ? it ’ s because of the way light is focussed by the lens in your eye . this lens , like magnifying glasses , eyeglasses , and contact lenses , is considered a thin lens . how lenses interact with light lenses bend light that passes through them . t...
the image will be on the same side of the lens from the object , and will be upright . the image will also be larger than the object . that means that the image distance will be negative .
for the practice question where we are asked to calculate the height of the apple image what is the equation used ?
we ’ ve all heard that there ’ s no sound in space , even though tons of movies and tv shows have you hearing everything from ships ’ engines to explosions . if there ’ s sound on earth , why wouldn ’ t there be sound in space ? the secret is in how sound travels . how does sound travel ? sound travels as waves of ener...
graphing sound waves we can show sound waves by graphing either how particles move ( displacement ) or how squished together they are ( density ) . but since density and pressure are related , a pressure vs time graph has the same form as a density vs time graph . if you ’ re looking at particle displacement , then you...
is n't wavelength displayed on a displacement versus distance/position graph ?
paris : narrow streets and barricades during each of the previous political revolts ( 1789 , 1830 , 1848 , and again in 1871 ) , sections of paris had succumbed to the revolutionaries . these successes were due in part to the political sympathies of the citizens of paris , but the crooked narrow lanes of the medieval c...
he plowed over the ancient , winding streets of the city ( the same narrow streets that had proved so useful to revolutionaries ) . in their place , he created broad straight boulevards that were impervious to the barricade—and , equally important , they could better accommodate the free movement of troops . the avenue...
this kind of urban renewal , done by leaders with absolute power , ostensibly to improve conditions for the people at the bottom of the society , and producing wide boulevards impervious to barricades and felicitous to the movement of troops , has been carried out in beijing after 1949 and was imposed on bucharest duri...
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
now you try it ! problem 4 problem 5 problem 6 why are these numbers important ? so why do we study complex numbers anyway ? believe it or not , complex numbers have many applications – electrical engineering and quantum mechanics to name a few !
would someone post a link to a good example of complex numbers being used directly to solve a real-world problem ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
for example , $ 3i $ , $ i\sqrt { 5 } $ , and $ -12i $ are all examples of pure imaginary numbers , or numbers of the form $ bi $ , where $ b $ is a nonzero real number . adding real numbers to these pure imaginary numbers creates even more numbers like $ 2+7i $ and $ 3-\sqrt { 2 } i $ . while these are not pure imagin...
where are complex numbers used in real life ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
for example , $ 3i $ , $ i\sqrt { 5 } $ , and $ -12i $ are all examples of pure imaginary numbers , or numbers of the form $ bi $ , where $ b $ is a nonzero real number . adding real numbers to these pure imaginary numbers creates even more numbers like $ 2+7i $ and $ 3-\sqrt { 2 } i $ . while these are not pure imagin...
using the same logic that all real numbers are complex , for example 52 = 52 + 0i , could n't we say that all imaginary numbers are complex as well ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
the $ \blued { \text { imaginary } } $ part of the number , or $ \blued b $ , is the real number coefficient of the pure imaginary number . the table below shows examples of complex numbers , with the real and imaginary parts identified . some people find it easier to identify the real and imaginary parts if the number...
is there an easy way to remember which numbers are real and complex and which are imaginary and complex ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
the $ \greend { \text { real } } $ part of the number , or $ \greend a $ , is the real number that is being added to the pure imaginary number . the $ \blued { \text { imaginary } } $ part of the number , or $ \blued b $ , is the real number coefficient of the pure imaginary number . the table below shows examples of c...
in a+bi , why is b considered the imaginary part ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
let 's take a closer look at this and try to understand how the number sets fit together . $ 9i $ is a pure imaginary number . yet , we can also express this number as $ \greend 0+\blued9i $ . so $ 9i $ is both a pure imaginary number and a complex number ! in fact , every pure imaginary number is also a complex number...
is 0 a real number or a pure imaginary number ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
believe it or not , complex numbers have many applications – electrical engineering and quantum mechanics to name a few ! from a purely mathematical standpoint , one cool thing that complex numbers allow us to do is to solve any polynomial equation . for example , the polynomial equation $ x^2-2x+5=0 $ does not have an...
so , if now we can solve any polynomial equation , does that mean that a function can have as its input imaginary and complex numbers ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
while these are not pure imaginary numbers , they are not real numbers either . instead , they belong to a set of numbers called the complex numbers . defining complex numbers a complex number is any number that can be written as $ \greend { a } +\blued { b } i $ , where $ i $ is the imaginary unit and $ \greend { a } ...
i.e that we extended the domain of our functions to complex numbers ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
so $ 9i $ is both a pure imaginary number and a complex number ! in fact , every pure imaginary number is also a complex number . similarly , $ -2 $ is a real number .
if x*i is an imaginary number , and x=o , then 0i=0 is also an imaginary number ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
in general , any nonzero complex number $ a+bi $ will also be ... ... a pure imaginary number if $ a=0 $ . ... a real number if $ b=0 $ . the diagram shows how the real , pure imaginary , and complex number sets fit together .
how can b = 0 be real but a = 0 be pure imaginary , as explained in the hints for problems 5 & 6 ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
so $ 9i $ is both a pure imaginary number and a complex number ! in fact , every pure imaginary number is also a complex number . similarly , $ -2 $ is a real number . yet , we can also express $ -2 $ as $ \greend { -2 } +\blued0i $ . so $ -2 $ is both a real number and a complex number ! in fact , every real number is...
when i found out 10.2 is a complex number i was like ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution .
is there a root of ( x^2 ) -1 in the 3-dimensional graph ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
let 's take a closer look at this and try to understand how the number sets fit together . $ 9i $ is a pure imaginary number . yet , we can also express this number as $ \greend 0+\blued9i $ .
what is the difference between a pure imaginary number and a imaginary number ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
in general , any nonzero complex number $ a+bi $ will also be ... ... a pure imaginary number if $ a=0 $ . ... a real number if $ b=0 $ . the diagram shows how the real , pure imaginary , and complex number sets fit together .
what type of number is 0 ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
in general , any nonzero complex number $ a+bi $ will also be ... ... a pure imaginary number if $ a=0 $ . ... a real number if $ b=0 $ . the diagram shows how the real , pure imaginary , and complex number sets fit together .
is `` 0 '' both imaginary and real ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
in fact , every pure imaginary number is also a complex number . similarly , $ -2 $ is a real number . yet , we can also express $ -2 $ as $ \greend { -2 } +\blued0i $ . so $ -2 $ is both a real number and a complex number !
what would happen if i had the square root of -2 and the square root of -18 and needed to find the sum ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution .
would we all be dead and hopeless or is there some way to achieve a quantity of i ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
yet , we can also express this number as $ \greend 0+\blued9i $ . so $ 9i $ is both a pure imaginary number and a complex number ! in fact , every pure imaginary number is also a complex number . similarly , $ -2 $ is a real number .
when does the step where , you alway divide by 4 then multiply the remainder by 4 then match to the exponent of the imaginary number , apply ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
yet , we can also express $ -2 $ as $ \greend { -2 } +\blued0i $ . so $ -2 $ is both a real number and a complex number ! in fact , every real number is also a complex number . in general , any nonzero complex number $ a+bi $ will also be ... ... a pure imaginary number if $ a=0 $ .
can someone help me if the complex number is like 3i - square root of -25 ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create infinitely many more new numbers . for example , $ 3i $ , $ i\sqrt { 5 } $ , and $ -12i $ are all examples of pure imaginary numbers , or numbers of the form $ bi $ , where $...
could you use imaginary numbers to explain extraneous roots ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
in general , any nonzero complex number $ a+bi $ will also be ... ... a pure imaginary number if $ a=0 $ . ... a real number if $ b=0 $ . the diagram shows how the real , pure imaginary , and complex number sets fit together .
so a number is complex if a + b > 0 , right ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create infinitely many more new numbers . for example , $ 3i $ , $ i\sqrt { 5 } $ , and $ -12i $ are all examples of pure imaginary numbers , or numbers of the form $ bi $ , where $...
anyone know how & why imaginary numbers were created ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
yet , we can also express $ -2 $ as $ \greend { -2 } +\blued0i $ . so $ -2 $ is both a real number and a complex number ! in fact , every real number is also a complex number . in general , any nonzero complex number $ a+bi $ will also be ... ... a pure imaginary number if $ a=0 $ .
i know this is unrelated , but what happens when you raise a number to the power of i ?
in the real number system , there is no solution to the equation $ x^2=-1 $ . in this lesson , we will study a new number system in which the equation does have a solution . the backbone of this new number system is the number $ i $ . $ \large i=\sqrt { -1 } $ by taking multiples of this imaginary unit , we can create ...
the $ \greend { \text { real } } $ part of the number , or $ \greend a $ , is the real number that is being added to the pure imaginary number . the $ \blued { \text { imaginary } } $ part of the number , or $ \blued b $ , is the real number coefficient of the pure imaginary number . the table below shows examples of c...
why only b is imaginary part and not i or bi ?
is there anything left to say about adam and eve , quite literally the oldest story in the book ? the engraving of adam and eve of 1504 by the german renaissance artist albrecht dürer recasts this familiar story with nuances of meaning and artistic innovation . in the picture , adam and eve stand together in a dense , ...
a german enthralled by the classical tradition the print allows dürer to express his personal and cultural concerns . proud of his german identity ( albert dvrer noricvs or “ albert dürer of nuremberg ” ) , the artist is nonetheless enthralled by italian and classical tradition . the german forest is ennobled by classi...
is the latin translation of `` albrecht '' , `` albert '' ?
is there anything left to say about adam and eve , quite literally the oldest story in the book ? the engraving of adam and eve of 1504 by the german renaissance artist albrecht dürer recasts this familiar story with nuances of meaning and artistic innovation . in the picture , adam and eve stand together in a dense , ...
this word play underpins the christian interpretation of the story of the fall of humanity by characterizing the virgin mary , mother of christ , as the antidote for eve ’ s sin in the garden of eden . the other animals bear other symbolic meanings . the elk , ox , rabbit , and cat exemplify the four humors or human pe...
is the reason that the snake and the bird not refrenced , in the analysis of the placement of the animals , because they are not important to the work , or was it just an oversight ?
is there anything left to say about adam and eve , quite literally the oldest story in the book ? the engraving of adam and eve of 1504 by the german renaissance artist albrecht dürer recasts this familiar story with nuances of meaning and artistic innovation . in the picture , adam and eve stand together in a dense , ...
dürer not only experienced the transformation from gothic to renaissance , he was an agent of that change . text by dr. bonnie j. noble additional resources : this print in the collection of the metropolitan museum of art a short video on this print from the clark art institute this work on the metropolitan museum of a...
was there a specific patron of the art piece ?
is there anything left to say about adam and eve , quite literally the oldest story in the book ? the engraving of adam and eve of 1504 by the german renaissance artist albrecht dürer recasts this familiar story with nuances of meaning and artistic innovation . in the picture , adam and eve stand together in a dense , ...
dürer not only experienced the transformation from gothic to renaissance , he was an agent of that change . text by dr. bonnie j. noble additional resources : this print in the collection of the metropolitan museum of art a short video on this print from the clark art institute this work on the metropolitan museum of a...
creating art was for albrecht durer , a sacred act.how does this print reflect that attitude ?
overview john f. kennedy narrowly won the 1960 presidential election against richard nixon by carefully cultivating the news media and crafting an effective public image . once in office , kennedy prioritized domestic economic growth , cutting taxes and boosting federal spending . during kennedy ’ s brief presidency , ...
those who listened to the debate on the radio thought that nixon had won , while those who watched on television agreed that kennedy was the winner. $ ^3 $ the election was extremely close , but kennedy ultimately triumphed over nixon by a slender margin . john f. kennedy as president once in office , kennedy embraced ...
why is the kennedy family referred to as a `` clan '' ?
overview john f. kennedy narrowly won the 1960 presidential election against richard nixon by carefully cultivating the news media and crafting an effective public image . once in office , kennedy prioritized domestic economic growth , cutting taxes and boosting federal spending . during kennedy ’ s brief presidency , ...
the minimum wage was raised and over \ $ 4 billion was allocated for housing construction . kennedy also announced that he would ask congress for a \ $ 10 billion tax cut unaccompanied by decreases in federal spending . he argued that an economic boom would result from such an approach , and thus tax revenues would be ...
why would somebody want to kill jfk ?
overview john f. kennedy narrowly won the 1960 presidential election against richard nixon by carefully cultivating the news media and crafting an effective public image . once in office , kennedy prioritized domestic economic growth , cutting taxes and boosting federal spending . during kennedy ’ s brief presidency , ...
kennedy also set the stage for increased us involvement in vietnam by supporting a military coup in south vietnam. $ ^7 $ kennedy 's assassination the presidency of john f. kennedy was tragically cut short by an assassin ’ s bullet on november 22 , 1963 , in dallas , texas . lee harvey oswald , an unstable ex-marine wi...
what is a motorcade and what does it look like ?
overview john f. kennedy narrowly won the 1960 presidential election against richard nixon by carefully cultivating the news media and crafting an effective public image . once in office , kennedy prioritized domestic economic growth , cutting taxes and boosting federal spending . during kennedy ’ s brief presidency , ...
during kennedy ’ s brief presidency , the united states experienced both foreign policy triumphs and tragedies , including the bay of pigs invasion and the cuban missile crisis . kennedy was assassinated in dallas , texas , on november 22 , 1963 . the election of 1960 the 1960 presidential election , which has been des...
what was kennedy doing in texas when he was assassinated , and who killed him ?
overview john f. kennedy narrowly won the 1960 presidential election against richard nixon by carefully cultivating the news media and crafting an effective public image . once in office , kennedy prioritized domestic economic growth , cutting taxes and boosting federal spending . during kennedy ’ s brief presidency , ...
during kennedy ’ s brief presidency , the united states experienced both foreign policy triumphs and tragedies , including the bay of pigs invasion and the cuban missile crisis . kennedy was assassinated in dallas , texas , on november 22 , 1963 . the election of 1960 the 1960 presidential election , which has been des...
in the last section about kennedy 's assassination , how did that affect people after the tragic moment and why was he assassinated in the first place ?
overview john f. kennedy narrowly won the 1960 presidential election against richard nixon by carefully cultivating the news media and crafting an effective public image . once in office , kennedy prioritized domestic economic growth , cutting taxes and boosting federal spending . during kennedy ’ s brief presidency , ...
those who listened to the debate on the radio thought that nixon had won , while those who watched on television agreed that kennedy was the winner. $ ^3 $ the election was extremely close , but kennedy ultimately triumphed over nixon by a slender margin . john f. kennedy as president once in office , kennedy embraced ...
was kennedy the first u.s. president to embrace keynesian economics ?
overview john f. kennedy narrowly won the 1960 presidential election against richard nixon by carefully cultivating the news media and crafting an effective public image . once in office , kennedy prioritized domestic economic growth , cutting taxes and boosting federal spending . during kennedy ’ s brief presidency , ...
those who listened to the debate on the radio thought that nixon had won , while those who watched on television agreed that kennedy was the winner. $ ^3 $ the election was extremely close , but kennedy ultimately triumphed over nixon by a slender margin . john f. kennedy as president once in office , kennedy embraced ...
how long was john f. kennedy president ?
overview john f. kennedy narrowly won the 1960 presidential election against richard nixon by carefully cultivating the news media and crafting an effective public image . once in office , kennedy prioritized domestic economic growth , cutting taxes and boosting federal spending . during kennedy ’ s brief presidency , ...
lee harvey oswald , an unstable ex-marine with ties to the soviet union and to the cuban émigré community in miami , shot kennedy from the window of a book depository while the president was riding in a convertible limousine as part of a motorcade . oswald himself was then murdered while in police custody , by jack rub...
why did jack ruby kill lee harvey oswald ?
overview john f. kennedy narrowly won the 1960 presidential election against richard nixon by carefully cultivating the news media and crafting an effective public image . once in office , kennedy prioritized domestic economic growth , cutting taxes and boosting federal spending . during kennedy ’ s brief presidency , ...
those who listened to the debate on the radio thought that nixon had won , while those who watched on television agreed that kennedy was the winner. $ ^3 $ the election was extremely close , but kennedy ultimately triumphed over nixon by a slender margin . john f. kennedy as president once in office , kennedy embraced ...
why did john f. want to get elected for president ?
overview john f. kennedy narrowly won the 1960 presidential election against richard nixon by carefully cultivating the news media and crafting an effective public image . once in office , kennedy prioritized domestic economic growth , cutting taxes and boosting federal spending . during kennedy ’ s brief presidency , ...
those who listened to the debate on the radio thought that nixon had won , while those who watched on television agreed that kennedy was the winner. $ ^3 $ the election was extremely close , but kennedy ultimately triumphed over nixon by a slender margin . john f. kennedy as president once in office , kennedy embraced ...
why was kennedy so popular ?
overview john f. kennedy narrowly won the 1960 presidential election against richard nixon by carefully cultivating the news media and crafting an effective public image . once in office , kennedy prioritized domestic economic growth , cutting taxes and boosting federal spending . during kennedy ’ s brief presidency , ...
this was partly due to the power of southern democrats in congress , who were threatening to block the president ’ s entire civil rights agenda . nevertheless , kennedy appointed several african americans to high-profile positions in the federal government and judiciary. $ ^6 $ in 1963 , he introduced comprehensive civ...
does the kennedy family still have a lot of influence on america ?
overview john f. kennedy narrowly won the 1960 presidential election against richard nixon by carefully cultivating the news media and crafting an effective public image . once in office , kennedy prioritized domestic economic growth , cutting taxes and boosting federal spending . during kennedy ’ s brief presidency , ...
kennedy also set the stage for increased us involvement in vietnam by supporting a military coup in south vietnam. $ ^7 $ kennedy 's assassination the presidency of john f. kennedy was tragically cut short by an assassin ’ s bullet on november 22 , 1963 , in dallas , texas . lee harvey oswald , an unstable ex-marine wi...
did the police find out why lee harvey oswald killed the president ?
overview john f. kennedy narrowly won the 1960 presidential election against richard nixon by carefully cultivating the news media and crafting an effective public image . once in office , kennedy prioritized domestic economic growth , cutting taxes and boosting federal spending . during kennedy ’ s brief presidency , ...
kennedy appeared charismatic and handsome , and was very effective at crafting a likable on-screen persona. $ ^2 $ nixon , on the other hand , frequently seemed sweaty , nervous , and brooding . those who listened to the debate on the radio thought that nixon had won , while those who watched on television agreed that ...
how did nixon manage to get close to kennedys votes , if kennedy was that appealing ?
overview john f. kennedy narrowly won the 1960 presidential election against richard nixon by carefully cultivating the news media and crafting an effective public image . once in office , kennedy prioritized domestic economic growth , cutting taxes and boosting federal spending . during kennedy ’ s brief presidency , ...
though kennedy ’ s vacillation and indecisiveness about the bay of pigs invasion had contributed to the missile crisis in the first place , his determined statesmanship helped defuse tensions and negotiate a peaceful resolution to the crisis . kennedy authorized the alliance for progress , a major trade and aid initiat...
what was the majority of america then republican or democratic ?
iranian metal bowls have a variety of shapes , decoration themes , and uses during the safavid period ( 1501-1736 ) . the iranian divination bowl with inscriptions and zodiac signs today in the brooklyn museum is decorated with unusual themes—a blend of religious , superstitious , and persian historical motifs . the pr...
around the convex hemispherical boss in the bottom of the interior ( above ) , there are three verses from the qur ’ an . these are divided with circular panels that also include zodiac signs . these verses are from surat an-nas ( chapter 110 ) of the qura ’ n , verses one , two , and three .
where did the zodiac originate ?
iranian metal bowls have a variety of shapes , decoration themes , and uses during the safavid period ( 1501-1736 ) . the iranian divination bowl with inscriptions and zodiac signs today in the brooklyn museum is decorated with unusual themes—a blend of religious , superstitious , and persian historical motifs . the pr...
it is still widely believed among muslims ( both sunnis and shiites ) , that reciting certain verses or making some du ‘ aā ( prayer ) will help guide you to the right path and help you seek god ’ s support . shiite divine text is also present on the bowl . for instance , the most visible inscription , on the neck of t...
what is the function of this bowl ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
from the beginning , popes and other leaders sought to encourage only professional men of war , whether kings , lords , knights , or simple men-at-arms , to go on crusade . and from the beginning , individuals of almost every other social class , age , and gender ignored this and wanted to go , too . the only people ex...
why did people of almost every age , class and gender desire to embark upon a crusade ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
muslims ( or areas under muslim governance ) continued to be targets , especially when they threatened or reconquered portions of the crusader states , but other targets included christian “ heretics ” ( for example , in southern france ) , the christian byzantine empire , and political opponents of the papacy within e...
was it a result of successful papal propaganda , or because those folks were fooled to think of crusading as a way of both seeking land and wealth from the outremer and god 's redemption ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
keep in mind though that crusading didn ’ t emerge from a vacuum , and many of the elements of crusading were circulating before 1095 . however , finding an end date for the crusades is quite difficult indeed . scholars used to stress that the heyday of crusading was before 1300 .
were the crusades primarily against muslims ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
keep in mind though that crusading didn ’ t emerge from a vacuum , and many of the elements of crusading were circulating before 1095 . however , finding an end date for the crusades is quite difficult indeed . scholars used to stress that the heyday of crusading was before 1300 .
were the crusades considered a success ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
going on crusade was not an “ easy out ” for younger sons ( as used to be thought ) nor was it a reliable treasure-hunting expedition ; it impoverished many more people than it profited . nonetheless , because of the spiritual and social rewards on offer for crusading , crusade leaders were never able to fully stop peo...
it says that `` crusade leaders were never able to fully stop people of both genders and all classes from accompanying armed parties on crusade '' but how would a woman justify herself going on a crusade ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
keep in mind though that crusading didn ’ t emerge from a vacuum , and many of the elements of crusading were circulating before 1095 . however , finding an end date for the crusades is quite difficult indeed . scholars used to stress that the heyday of crusading was before 1300 .
are there modern examples of crusades ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
keep in mind though that crusading didn ’ t emerge from a vacuum , and many of the elements of crusading were circulating before 1095 . however , finding an end date for the crusades is quite difficult indeed . scholars used to stress that the heyday of crusading was before 1300 .
what role did women play in the crusades ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
in still other places , again in northern europe but also malta , the military orders—armed religious orders ( most famously the knights templar ) —set up independent , or virtually independent states dedicated to perpetual crusading . participants who went on crusade ? from the beginning , popes and other leaders soug...
why is the 4th crusade mentioned a lot in history books but michael viii palaiologos , the man who recapture it is not ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
we should also remember that the levant and iberia contained any number of local christians , jews , and other religious groups , and they were not always exempted from crusader violence , even though it was held to be wrong to persecute or kill fellow christians and jews . after the second crusade , crusading continue...
why is there such a gap between the first crusade and the second ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
keep in mind though that crusading didn ’ t emerge from a vacuum , and many of the elements of crusading were circulating before 1095 . however , finding an end date for the crusades is quite difficult indeed . scholars used to stress that the heyday of crusading was before 1300 .
why were n't the crusades called `` genocide '' attempts ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
rather , it means that contemporaries believed that the wars on all three fronts together constituted a larger endeavor . we should also remember that the levant and iberia contained any number of local christians , jews , and other religious groups , and they were not always exempted from crusader violence , even thou...
why did the assassins of masyaf castle try to kill saladin ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
participants who went on crusade ? from the beginning , popes and other leaders sought to encourage only professional men of war , whether kings , lords , knights , or simple men-at-arms , to go on crusade . and from the beginning , individuals of almost every other social class , age , and gender ignored this and want...
was there some sort of ritual that the knights had to go through too go crusading ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
after the second crusade , crusading continued to expand and evolve . muslims ( or areas under muslim governance ) continued to be targets , especially when they threatened or reconquered portions of the crusader states , but other targets included christian “ heretics ” ( for example , in southern france ) , the chris...
was there a ritual to `` forgive '' the crime or was it justified because the targets were `` sinners '' ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
who was in control of jerusalem prior to the first crusade ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
by the time the second crusade rolled around ( 1146-1149 ) crusading had already expanded dramatically . the second crusade took place on three fronts : against muslims in the levant , against pagans in northern europe , and against muslims on the iberian peninsula ( modern day spain and portugal ) . this does not mean...
is the conflict today with radical muslims against christians considered `` modern crusades '' ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
nonetheless , because of the spiritual and social rewards on offer for crusading , crusade leaders were never able to fully stop people of both genders and all classes from accompanying armed parties on crusade , and it is fair to say that many expeditions , especially those to the levant , included a wide range of age...
in fact , how would dr. throop differentiate between viking raids and crusading ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
keep in mind though that crusading didn ’ t emerge from a vacuum , and many of the elements of crusading were circulating before 1095 . however , finding an end date for the crusades is quite difficult indeed . scholars used to stress that the heyday of crusading was before 1300 .
what were the causes of the crusades ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
muslims ( or areas under muslim governance ) continued to be targets , especially when they threatened or reconquered portions of the crusader states , but other targets included christian “ heretics ” ( for example , in southern france ) , the christian byzantine empire , and political opponents of the papacy within e...
also , the what crusade did the battle of hattin , saladin 's greatest victory , come under ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
keep in mind though that crusading didn ’ t emerge from a vacuum , and many of the elements of crusading were circulating before 1095 . however , finding an end date for the crusades is quite difficult indeed . scholars used to stress that the heyday of crusading was before 1300 .
what was the cause of the crusades ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
keep in mind though that crusading didn ’ t emerge from a vacuum , and many of the elements of crusading were circulating before 1095 . however , finding an end date for the crusades is quite difficult indeed . scholars used to stress that the heyday of crusading was before 1300 .
the crusades are holy wars , if you will , but does n't that go against the teachings of jesus ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
keep in mind though that crusading didn ’ t emerge from a vacuum , and many of the elements of crusading were circulating before 1095 . however , finding an end date for the crusades is quite difficult indeed . scholars used to stress that the heyday of crusading was before 1300 .
what was the meaning behind the crusades ?
setting a timeline in some ways , setting a beginning date for the crusading movement is relatively easy . the first crusade was preached by pope urban ii in 1095 . several different expeditions responded to this appeal , but the general dates for the first crusade are 1096-1099 , when the city of jerusalem was conquer...
we should also remember that the levant and iberia contained any number of local christians , jews , and other religious groups , and they were not always exempted from crusader violence , even though it was held to be wrong to persecute or kill fellow christians and jews . after the second crusade , crusading continue...
could the fighting after the second crusade be considered a 3rd crusade in technical terms ?