Complex Analysis: brach of the square root

[tarheelborn]

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.

 

[Quinzio]

Use

"[itex]1+1=2[/itex]"

instead of

"[tex]1+1=2[/tex]"

 

[tarheelborn]

Thanks; I wondered what was up with that...