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help-1
9bfb1292b6cb4f9d844baf81546ce20d
692,654,133,785,657,300
Alexander42
01/21/2022 09:56:02
did you really move Zenith around the whole circle? Then it should be a circle
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
700,565,896,103,592,000
γ•γ‚ˆγ‚Š
01/21/2022 09:57:04
Wait nvm
1
0
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
700,565,896,103,592,000
γ•γ‚ˆγ‚Š
01/21/2022 09:57:11
Let me redraw
1
0
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
700,565,896,103,592,000
γ•γ‚ˆγ‚Š
01/21/2022 09:58:12
Oh wait I did a misconception
1
0
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
700,565,896,103,592,000
γ•γ‚ˆγ‚Š
01/21/2022 09:58:33
Yes it's a circle
1
0
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
692,654,133,785,657,300
Alexander42
01/21/2022 09:59:31
this circle is the "summon zone" from the exercise, which has area 5
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
700,565,896,103,592,000
γ•γ‚ˆγ‚Š
01/21/2022 10:00:49
Ok then.
1
0
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
692,654,133,785,657,300
Alexander42
01/21/2022 10:01:22
now you should be able to find out the area of the circle you started with
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1
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
700,565,896,103,592,000
γ•γ‚ˆγ‚Š
01/21/2022 10:03:23
Is it also 5 or I'm missing something crucial
1
0
212,479,607,071,440,900
Luca
7715
Luca
false
205,546
help-1
9bfb1292b6cb4f9d844baf81546ce20d
692,654,133,785,657,300
Alexander42
01/21/2022 10:03:57
the summon zone should be much smaller
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
692,654,133,785,657,300
Alexander42
01/21/2022 10:04:33
it should look something like this
https://cdn.discordapp.c…9626/unknown.png
unknown.png
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
700,565,896,103,592,000
γ•γ‚ˆγ‚Š
01/21/2022 10:06:37
OHHHHH, How do you get the area outside the zone either, This is interesting.
1
0
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
692,654,133,785,657,300
Alexander42
01/21/2022 10:10:28
if zenith is right on the opposite side of Ur, then Viz is in the center of the big circle (labelled A in my picture). Does this tell you something about the diameters of the two circles?
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
700,565,896,103,592,000
γ•γ‚ˆγ‚Š
01/21/2022 10:14:46
The diameter of the outside is double the summon diameter?.
1
0
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
692,654,133,785,657,300
Alexander42
01/21/2022 10:14:55
correct
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1
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
692,654,133,785,657,300
Alexander42
01/21/2022 10:15:07
what does this mean for the area?
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
700,565,896,103,592,000
γ•γ‚ˆγ‚Š
01/21/2022 10:17:33
It also doubles?
1
0
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
692,654,133,785,657,300
Alexander42
01/21/2022 10:17:52
no
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
692,654,133,785,657,300
Alexander42
01/21/2022 10:18:33
the area of a circle is pi*(diameter/2)^2
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1
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
700,565,896,103,592,000
γ•γ‚ˆγ‚Š
01/21/2022 10:21:18
Wait no, It gets bigger by 4 times
1
0
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
692,654,133,785,657,300
Alexander42
01/21/2022 10:21:56
yes
0
1
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
692,654,133,785,657,300
Alexander42
01/21/2022 10:22:26
so it has which area?
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1
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
700,565,896,103,592,000
γ•γ‚ˆγ‚Š
01/21/2022 10:23:23
20
1
0
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
692,654,133,785,657,300
Alexander42
01/21/2022 10:24:25
yes
0
1
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205,546
help-1
9bfb1292b6cb4f9d844baf81546ce20d
692,654,133,785,657,300
Alexander42
01/21/2022 10:25:20
so the area in the magic circle without the summoning area is 20-5=15
0
1
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
700,565,896,103,592,000
γ•γ‚ˆγ‚Š
01/21/2022 10:26:34
So The Area Outside the Summoning Area is 15, THANKS, It clears a Lot of Misconception on Geometry.
1
0
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
692,654,133,785,657,300
Alexander42
01/21/2022 10:26:54
you're welcome
0
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help-1
9bfb1292b6cb4f9d844baf81546ce20d
700,565,896,103,592,000
γ•γ‚ˆγ‚Š
01/21/2022 10:27:40
.close
1
0
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help-1
16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 10:30:23
Hello! i am wondering about a question on complex numbers, I have 2/(1-e^(ix)) and the book says to multiply top and bottom by e^(-ix/2) and am unsure why that is?
1
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16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 10:42:43
what happens when you do it?
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help-1
16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 10:43:35
it's not a theorem, it's just a way to manipulate fractions of complex numbers that comes up in many contexts. As to why it would be useful to do so, well, it depends on the context.
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help-1
16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 10:46:24
why is it a way of doing it? could you tell me what it achieves or why it couldnt be /3 or /4 etc?
1
0
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help-1
16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 10:47:04
i know its technically multiplying it by 1 but e^(-ix/2) is just really random to me
1
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16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 10:47:30
did you try doing it and seeing what it looks like?
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help-1
16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 10:48:36
yeah, 2e^(-ix/2)/(e^(-x/2) - e^(ix/2))
1
0
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help-1
16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 10:49:05
oh, I'm sorry, I missed the fraction in the question!
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help-1
16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 10:49:18
I was too lazy to put on my glasses
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16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 10:49:27
can you take a picture/screenshot of the exercise?
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16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 10:50:15
sure just a minute :))
1
0
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help-1
16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 10:51:22
https://cdn.discordapp.c…942A849A956.jpeg
6AF2001D-75E4-4F58-AC90-3942A849A956.jpeg
1
0
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16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 10:51:28
.rotate
0
1
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16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 10:51:40
,rotate
0
1
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16492a517f3245ff8d6a3c4e810c35ba
510,789,298,321,096,700
TeXit
01/21/2022 10:51:50
https://cdn.discordapp.c…981845954560.png
205675981845954560.png
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help-1
16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 10:52:47
its step 2 that im struggling with, after that its absolutely fine
1
0
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help-1
16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 10:53:23
i abbreviated x = pi/n
1
0
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help-1
16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 10:54:08
It's because you want to use a trigonometric identity that involves the term $e^{i\theta} - e^{-i\theta}$
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help-1
16492a517f3245ff8d6a3c4e810c35ba
510,789,298,321,096,700
TeXit
01/21/2022 10:54:10
**gfauxpas**
https://cdn.discordapp.c…981845954560.png
205675981845954560.png
0
1
null
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205,547
help-1
16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 10:54:40
and e^ix/2 satisfies that?
1
0
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help-1
16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 10:54:52
could you explain how?
1
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help-1
16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 10:55:12
Let's take a simple example, as soon as I take my bagels out of the oven because the timer just rang and I dont want them to burn
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help-1
16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 10:55:31
no problem :))
1
0
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16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 10:57:11
okay
0
1
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help-1
16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 10:58:05
Let's say I want to analyze an expression like
0
1
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16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 10:59:05
$e^{i \pi/4} + e^{-i \pi/4}$
0
1
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help-1
16492a517f3245ff8d6a3c4e810c35ba
510,789,298,321,096,700
TeXit
01/21/2022 10:59:17
**gfauxpas**
https://cdn.discordapp.c…981845954560.png
205675981845954560.png
0
1
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205,547
help-1
16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 10:59:28
well, I know the trig idendity:
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help-1
16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 10:59:45
$\cos(x) = \frac{e^{ix} + e^{-ix}}2$
0
1
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help-1
16492a517f3245ff8d6a3c4e810c35ba
755,831,671,588,126,700
RepliedPencil
01/21/2022 10:59:51
e^ix = cosx + isinx :p
0
1
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help-1
16492a517f3245ff8d6a3c4e810c35ba
510,789,298,321,096,700
TeXit
01/21/2022 10:59:52
**gfauxpas**
https://cdn.discordapp.c…981845954560.png
205675981845954560.png
0
1
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null
205,547
help-1
16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 11:00:07
oh yeah ive seen that before
1
0
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16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 11:00:09
so I can take my expression and write
0
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help-1
16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 11:00:22
it's the same thing as what Pencil said, of course, just solved for cosine
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help-1
16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 11:00:29
I can show you how its derived
0
1
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help-1
16492a517f3245ff8d6a3c4e810c35ba
755,831,671,588,126,700
RepliedPencil
01/21/2022 11:00:29
Yes ^^
0
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help-1
16492a517f3245ff8d6a3c4e810c35ba
755,831,671,588,126,700
RepliedPencil
01/21/2022 11:01:18
U can also derive it from Maclaurin expansions too
0
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help-1
16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 11:01:19
$e^{i \pi/4} + e^{-i \pi/4}= 2 \times \frac{e^{i \pi/4}+ e^{-i\pi/4} }2$
0
1
869,532,694,688,706,600
EpsilonNought
8684
EpsilonNought
false
205,547
help-1
16492a517f3245ff8d6a3c4e810c35ba
510,789,298,321,096,700
TeXit
01/21/2022 11:02:18
**gfauxpas**
https://cdn.discordapp.c…981845954560.png
205675981845954560.png
0
1
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205,547
help-1
16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 11:02:35
and then I can say that this is equal to $2 \cos (\pi/4)$
0
1
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help-1
16492a517f3245ff8d6a3c4e810c35ba
510,789,298,321,096,700
TeXit
01/21/2022 11:02:38
**gfauxpas**
https://cdn.discordapp.c…981845954560.png
205675981845954560.png
0
1
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205,547
help-1
16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 11:03:47
so 2cos(pi/4) = e^(i*pi/4) + e^(-i pi/4)?
1
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help-1
16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 11:03:58
Same thing here, except with this
https://cdn.discordapp.c…7410/unknown.png
unknown.png
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help-1
16492a517f3245ff8d6a3c4e810c35ba
755,831,671,588,126,700
RepliedPencil
01/21/2022 11:04:05
Yes
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help-1
16492a517f3245ff8d6a3c4e810c35ba
755,831,671,588,126,700
RepliedPencil
01/21/2022 11:04:39
Basically 2cosx = e^ix + e^-ix (general identity)
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help-1
16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 11:05:21
The easiest way to prove these identities is to solve the system of equations for sine and cosine: $\begin{cases} e^{i \theta} = \cos \theta + i \sin \theta \\ e^{-i \theta} = \cos \theta - i \sin \theta \end{cases}$ because sine is odd and cosine is even
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16492a517f3245ff8d6a3c4e810c35ba
510,789,298,321,096,700
TeXit
01/21/2022 11:05:59
**gfauxpas**
https://cdn.discordapp.c…981845954560.png
205675981845954560.png
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16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 11:07:41
ah okay, but in the case of the question, how does e^-i*pi/2n work in all this when the complex number is e^(i *pi/n)
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16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 11:08:02
the things youve shown me, how do they cause that to happen?
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16492a517f3245ff8d6a3c4e810c35ba
755,831,671,588,126,700
RepliedPencil
01/21/2022 11:08:05
Yes ^^^
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16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 11:10:01
theyre both 2 different coeffiecients, one is -i*pi/2n and one is just i * pi/n
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16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 11:10:14
so what is the cause exactly?
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16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 11:12:50
could you not just multiply by -i*pi/n?
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16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 11:14:35
for the identity to work, you need "x" to be the same in both e^(ix) and e^(-ix)
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16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 11:15:00
so the factor of 1/2 splits the number in half so that it's the same inside each e in the denominator
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16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 11:15:48
oh is that it? its just getting the same exponent in the denominator??
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help-1
16492a517f3245ff8d6a3c4e810c35ba
205,675,981,845,954,560
gfauxpas
01/21/2022 11:16:42
yes
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help-1
16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 11:17:06
Oh i see! it all makes sense now! Thank you both for your help!
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16492a517f3245ff8d6a3c4e810c35ba
934,103,418,585,362,400
Samjamhawk3y3
01/21/2022 11:17:43
i really appreciate your patience and kindness, i hope you have a great day :))
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16492a517f3245ff8d6a3c4e810c35ba
755,831,671,588,126,700
RepliedPencil
01/21/2022 11:18:10
Yw ^^
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9870c8cbb9614bf7bf79ca16ec5a9dae
369,968,522,635,509,760
emerald
01/21/2022 12:37:53
I’m so stuck
https://cdn.discordapp.c…256/IMG_0180.png
IMG_0180.png
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9870c8cbb9614bf7bf79ca16ec5a9dae
456,226,577,798,135,800
Deleted User
01/21/2022 12:39:18
Note that differentiation of 1/x is not ln(x)
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9870c8cbb9614bf7bf79ca16ec5a9dae
369,968,522,635,509,760
emerald
01/21/2022 12:40:14
oh wait right
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9870c8cbb9614bf7bf79ca16ec5a9dae
369,968,522,635,509,760
emerald
01/21/2022 12:43:40
How would you get rid of the e^1/x
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9870c8cbb9614bf7bf79ca16ec5a9dae
869,532,694,688,706,600
EpsilonNought
01/21/2022 12:44:22
Hmm
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9870c8cbb9614bf7bf79ca16ec5a9dae
869,532,694,688,706,600
EpsilonNought
01/21/2022 12:44:35
Use 1/x = u
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help-1
9870c8cbb9614bf7bf79ca16ec5a9dae
869,532,694,688,706,600
EpsilonNought
01/21/2022 12:44:46
And solve
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help-1
9870c8cbb9614bf7bf79ca16ec5a9dae
869,532,694,688,706,600
EpsilonNought
01/21/2022 12:45:05
Du/dx will be -1/x^2
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help-1
9870c8cbb9614bf7bf79ca16ec5a9dae
869,532,694,688,706,600
EpsilonNought
01/21/2022 12:45:08
There u go
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help-1
9870c8cbb9614bf7bf79ca16ec5a9dae
869,532,694,688,706,600
EpsilonNought
01/21/2022 12:45:18
Problemo solved mon amigo
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help-1
9870c8cbb9614bf7bf79ca16ec5a9dae
869,532,694,688,706,600
EpsilonNought
01/21/2022 12:45:21
@emerald
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help-1
9870c8cbb9614bf7bf79ca16ec5a9dae
369,968,522,635,509,760
emerald
01/21/2022 12:45:40
Ok thanks let me piece it together
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