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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:11:46
The inputs are represented by a line in a normal graph
0
1
null
null
null
null
null
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:11:52
the x-axis
0
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:11:58
Here the inputs are represented by a plane
0
1
373,884,980,977,336,300
Remavas
3737
Remavas
false
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:12:05
whut
1
0
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null
null
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:12:23
ooh ig i got it
1
0
706,934,233,012,371,600
Ansh_
3502
Arya
false
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:12:29
but not the 4d thing
1
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:12:55
Well, if you have 1 dimension for the input + 1 dimension for the output (normal graph), you need 2 dimensions total
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Syst3ms
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:13:03
Which is what happens, you draw 2d graphs
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
826,318,983,413,366,800
Cogwheels of the mind
03/06/2022 08:13:25
The real part of output is the third dimension, and imaginary part of output is denoted by color
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1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:13:43
yea ik why the curvy thing then
1
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:14:01
Yeah, in theory you'd need 4 dimensions, but since that's not something we can visualize, so color is used
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:14:07
define "curvy thing"
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:14:44
why don’t we have x,y,z and another in color
1
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:15:06
oh x,y is one plane?
1
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:15:15
really confused
1
0
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:16:21
Yeah
0
1
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:16:30
The complex numbers are described by x+iy
0
1
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:16:50
So if you want to look at every possible input, you need to look at every possible value of x and y
0
1
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:17:02
Which takes a whole plane to do
0
1
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:17:15
(but if you have a way to show it with a single line, by all means tell me)
0
1
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:18:51
damn i still don’t get it
1
0
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:19:22
Let's start with normal graphs again
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1
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:19:27
okay!!
1
0
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:19:42
The point of a graph is to show the output of the function for every possible input
0
1
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:19:53
hm
1
0
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:20:01
here's a sample graph
https://cdn.discordapp.c…641487902/iu.png
iu.png
0
1
231,419,337,771,057,150
Lenny
5476
Lenny
false
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:20:09
So, we want to show what the function's value is for any value of x
0
1
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:20:17
yea
1
0
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:20:26
So we must have some way to represent what the function's input is on the graph
0
1
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1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:20:31
Here's, it's done with the x-axis
0
1
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:20:43
mhm
1
0
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:20:54
If we're at 1 on the x-axis, we're representing f(1)
0
1
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null
null
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:20:55
etc
0
1
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:21:03
yea
1
0
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:21:10
And then, the y-axis represents the output
0
1
null
null
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null
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1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:21:14
yep
1
0
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null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:21:22
Now let's go to complex numbers
0
1
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null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:21:32
We still want to represent the function's value at every point
0
1
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:21:55
that is, we want to be able to represent f(x+iy) for every *real* x and y
0
1
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:22:08
because that describes every single complex number
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1
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:22:15
that’s 3d right
1
0
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1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:22:26
Not so fast
0
1
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1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:22:33
hm
1
0
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:22:50
So, instead of the x-axis, to describe the input you need to show both x and y
0
1
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null
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null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:23:04
(no relation to the x and y of a normal graph, there are only that many letters i can use)
0
1
null
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null
null
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1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:23:04
why
1
0
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:23:28
Every complex number can be written z=x+iy
0
1
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null
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null
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1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:24:00
On a normal graph, you need the x-axis to be able to point at a horizontal position and say "lookie, here, it represents the value of f(2)"
0
1
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null
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null
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1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:24:05
or f(1), or f(whatever)
0
1
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:24:18
mhm
1
0
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:24:40
But here, you also need to be able to point at *something* and say "lookie, here it represents the value of f(x+iy)"
0
1
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:24:47
x+iy being some complex number
0
1
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null
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1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:24:58
be it f(1) or f(i) or f(256-35i), whatever
0
1
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null
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1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:25:18
isn’t i imaginary and 1+i complex?
1
0
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null
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:25:38
Not quite
0
1
193,692,307,453,771,780
Syst3ms
9959
Syst3ms
false
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:25:48
the complex numbers are all the numbers that can be written x+iy
0
1
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null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:26:00
That includes the real numbers (take y=0), as well as the imaginary numbers (take x=0)
0
1
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1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:26:12
but 1+0i is 1 is 1 complex too then?
1
0
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:26:14
So imaginary and real numbers are just specific kinds of complex numbers
0
1
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1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:26:16
Indeed
0
1
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:26:25
Real numbers are a part of the complex numbers
0
1
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:26:30
ooh
1
0
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:28:25
Anyway, from the description of the complex numbers i just gave, it would be really convenient to be able to spot both x and y on the inputs
0
1
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:28:34
Because if you know x and y, you know x+iy, so you know the input
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1
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:29:15
but x+iy is just x+iy
1
0
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1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:30:26
What do you mean by that
0
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:30:43
we can’t combine i and normal numbers
1
0
null
null
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null
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:30:44
idkk
1
0
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:32:52
Please try to express what's holding you back here
0
1
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:32:56
It's important we address it
0
1
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1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:39:05
idk
1
0
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:39:30
Okay, on second thought this series might have not been the best recommendation
0
1
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:39:35
My apologies
0
1
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:39:48
the first 10 episodes were pretty cool
1
0
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:39:55
but then it got really complicated
1
0
null
null
null
null
null
1,061
help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:40:16
I think it's more targeted towards people who have already manipulated complex numbers
0
1
null
null
null
null
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:40:29
So I'll just fall back on the good old and reliable Khan Academy
0
1
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null
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null
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:40:36
oh no
1
0
null
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:41:40
They have this playlist on the introduction to complex numbers, that starts off very gently with imaginary numbers. Take it step by step if you need to, because there are many videos in this playlist
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:41:43
https://www.youtube.com/playlist?list=PLXSlB4yMaoJtM2gG5Mas5mMjwX_B51vsB
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:42:16
khan academy can get really hard because i’m not english
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:42:23
I see
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:42:25
What language?
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:42:28
german
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:42:32
I see
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:42:39
even tho u wanna do math in english
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:42:51
so i mostly learn on discord cuz i can ask questions
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:42:53
Well, you can always try to look up introductions to complex numbers in German if you want
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:43:10
It's a common topic, I'd be shocked to learn there are no comprehensive introductions to it
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:43:49
can u show me how? cuz videos ain’t so fun :p
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:44:17
i honestly just typed "complex number introduction" in youtube and found something that looked long enough
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:44:28
"komplexe zahlen erklärt" could do the trick
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:44:41
search it on google if you don't want videos, whatever floats your boat
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:45:12
can i dm u for questions?
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:46:04
If you really get stuck one something you can try, but I'm not going to be available very often
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:46:16
(actually, past this weekend, basically never for the coming month)
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:46:20
So yeah
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:46:25
wow xD
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
231,419,337,771,057,150
Lenny
03/06/2022 08:47:09
soo wdym with manipulating complex numbers
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help-10
1fe1ab238bdb4803a992a8e6a5ef25a7
193,692,307,453,771,780
Syst3ms
03/06/2022 08:47:32
Just getting used to the concept and learning what you can do with them, in general
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