(adsbygoogle = window.adsbygoogle || []).push({}); In the complex plane, let C be the circle |z| = 2 with positive (counterclockwise) orientation. Show that:

[tex]\int _C \frac{dz}{(z-1)(z+3)^2} = \frac{\pi i}{8}[/tex]

This isn't homework, it was a problem in one of the practice GREs. It looks like a straightforward application of the residue theorem, the only problem is that I never understood the second half of complex analysis? The only pole of the integrand contained in the interior of C is 1, so I have to find the residue of the integrand at 1? What's a residue, and how do I find it? Mathworld gives a definition in terms of the Laurent series, but I'm sure there's a simpler way when it comes to basic rational functions like these. And once I have the residue, what do I do, multiply by [itex]2\pi i[/itex]? Thanks.

**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!

# Homework Help: Residue Theorem

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