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 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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