Hi, I'm stuck on this problem:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int{\frac{1}{z^4+1}}[/tex]

Writing it as a product of its roots, we get:

[tex]\frac{1}{(z-e^{\frac{i\pi}{4}})(z-e^{\frac{3i\pi}{4}})(z-e^{\frac{5i\pi}{4}})(z-e^{\frac{7i\pi}{4}})}[/tex]

Then applying Cauchy's residue theorem for simple poles:

[tex]\mbox{Res}(f,c)=\lim_{z\rightarrow c}(z-c)f(z)[/tex]

It's here that I'm stuck - I've got the poles and the function, how do I get the residues in this case?

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# Contour Integration: finding residues

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