- #1

Jufro

- 92

- 8

## Homework Statement

**Essential Mathematical Methods for the Physics Sciences**Problem 15.7

Show that if f(z) has a simple zero at z

_{0}then 1/ f(z) has a residue of 1/f'(z

_{0}). Then use this information to evaluate:

∫ sinθ/(a- sinθ) dθ, where the integral goes from -∏ to ∏.

## Homework Equations

The book has further hints:

The unit circle has only one pole at z= i*a-i(a

^{2}-1)^1/2 and therefore has a residue of -i/2 *(a

^{2}-1)

^{-1/2}.

## The Attempt at a Solution

The first part is:

1/f(z) has a simple pole at z

_{0}leaving the residue to be lim

_{z→z0}(z-z

_{0}) * 1/f(z) = 1/f'(z

_{0}) by definition of the derivative.

But using this information to do the integral is escaping me. Can anyone just help me understand how to use the hint. I don't actually need the whole step by step guide to the integral.