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## Homework Statement

Hi all.

My question has to do with integrating rational functions over the unit circle. My example is taken from here (page 2-3): http://www.maths.mq.edu.au/%7Ewchen/lnicafolder/ica11.pdf

We wish to integrate the following

[tex]

\int_0^{2\pi } {\frac{{d\theta }}{{a + \cos \theta }}}.

[/tex]

According to the .pdf, we integrate along a unit circle, and we define [itex] z = e^{i\theta}[/itex]. When rewriting the integrating using

*z*, we find that the integrand has to poles: One inside the unit circle and one outside. When we use the residue theorem, we

**only**use the pole

**inside**the unit circle.

**My question**: How are we even allowed just to say: "We choose only to integrate along a unit circle, and thus we only look at poles inside this circle"? If I claim that we should integrate along a circle big enough to include all poles, then who can say argument against my claim?

I hope you understand me. Niles.