# Homework Help: Complex Analysis

1. Feb 8, 2012

### tarheelborn

1. The problem statement, all variables and given/known data
Demonstrate that a domain $D\in\mathbb{C}$ is simply connected if and only if, for every function $f$ which is analytic and free of zeroes in $D$, a branch of the square root of $f$ exists in $D$.

2. Relevant equations

3. The attempt at a solution

I know that by definition, every function f which is analytic and free of zeroes in D, a branch of log(f(z)) exists in D and that this implies the existence of $p^{th}$ roots of that function. I am not sure how to get from here to square roots, though.

Last edited by a moderator: Feb 9, 2012