(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given a complex valued function [tex]f(z) = 1/z^2+1[/tex] show the area for which its holomorphic?

2. Relevant equations

I know that if [tex]f:\Omega \rightarrow \mathbb{C}[/tex] and [tex]z_0 \in \Omega[/tex]

then [tex]f'(z_0) = \lim_{z \rightarrow z_0} \frac{f(z)-f(z_0)}{z-z_0}[/tex]

if the limit exists then f is holomorphic at the point [tex]z_0[/tex]....

3. The attempt at a solution

To show the area for which f is holomorphic isn't this simply to check if the definition above can be applied to every [tex]z_0[/tex] of f?? Or am I missing something here?

where the two possiblites for [tex]z_0 = \pm i[/tex] or is it simply that f is holomorphic on the area [tex]\Omega - \{\pm i\}[/tex] ??

Best Regards

Susanne

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# Homework Help: Question regarding holomorphic functions

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