Taylor Series Expansion About the Point i

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Taylor Series Expansion About the Point "i"

Homework Statement



Calculate the radius of convergence of the Taylor series for

\frac{1}{z^2-2z+2}

about the point i.

The Attempt at a Solution



I can find the radius of convergence if I can determine the expansion but I can't seem to spot the pattern...

Any help will be appreciated (please see attached).
 

Attachments

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how about consdering where the poles of the function are...
 


We haven't actually covered that yet, but I'll have a look thanks!
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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