# Homework Help: Complex Analysis: brach of the square root

1. Nov 29, 2011

### tarheelborn

1. The problem statement, all variables and given/known data
Let $f$ be a quadratic polynomial function of $z$ with two different roots $z_1$ and $z_2$. Given that a branch $z$ of the square root of $f$ exists in a domain $D$, demonstrate that neither $z_1$ nor $z_2$ can belong to $D$. If $f$ had a double root, would the analogous statement be true?

2. Relevant equations
We say that a branch $g(z)$ of the $p^{th}$ root of $z$ exists on $D$ if $g(z)$ is continuous and $g(z)^{p}=z$ for every $z \in D$.

3. The attempt at a solution
I am really not sure at all how to begin this proof. I would appreciate a nudge to get started. Thank you.

Last edited: Nov 29, 2011
2. Nov 29, 2011

### Quinzio

Use
Code (Text):
"$1+1=2$"
"$$1+1=2$$"