Use Laurent series to find the residue

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This video shows how to find the residue of the function f(z) where z=a+bi and i=sqrt(-1) for the the function at 1 .
First part is to find the Laurent series at 1 and then find the z^-1 coefficient .
this gives us res(f,1) .
Here the function is 1/(z(z-1)^2)
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  1. sumchief
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Комментарии
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Great video, but sir, your "z" is a bit hard to distinguish from a "2".

TheLeontheking
Автор

Hi,

isnt the residue of this function 1 though?
you never made the change of base back?

by residue theorem, the singularty at 0 is of order 1 - simple pole. then lim z->0 of 1/(z-1)^2 = 1.

so you found the residue of the function at 1, which is -1.

be careful with your change of base.

gokudegrees
Автор

The title of the video: res(f, 1)
It isn't a simple pole, henc res(f, 1) equal to zero

jasonlin