# Complex Analysis: brach of the square root

## Homework Statement

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?

## Homework 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 $z \in D$.

## 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:

Related Calculus and Beyond Homework Help News on Phys.org
Use
Code:
"$1+1=2$"
"$$1+1=2$$"