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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Contour Integration: finding residues

**Physics Forums | Science Articles, Homework Help, Discussion**