# Homework Help: Residue Theorem Applications

1. Aug 10, 2014

### itsnogood

Hi, first post here. I'm having some trouble with contour integration. Basically here's the question:

Contour Integral of

1+z dz
(z-1)(z2+9)

There are three cases:

l z l = 2
l z+1 l = 1
l z-$\iota$ l = 3

Is each case a straightforward application of the residue theorem? Also, reading up in my textbook the poles should be contained within the contour so does on the boundary count?

2. Aug 10, 2014

### vela

Staff Emeritus
You should take a little time and learn LaTeX. It's not very difficult.
$$\int_C \frac{1+z}{(z-1)(z^2+9)}\,dz$$
There's a good tutorial here: https://www.physicsforums.com/showthread.php?p=3977517#post3977517

Yup.

No, the pole needs to be inside the contour. If it's on the contour, you have to treat it differently.