# Homework Help: Question about Riemann Surface Problem

1. Feb 14, 2016

### Crush1986

1. The problem statement, all variables and given/known data
$$f(z)=z^\frac{3}{2}$$ find the branch points, branch cuts, and Riemann sheet structure.
2. Relevant equations
none

3. The attempt at a solution
So, I converted this to complex exponential form $$r^\frac{3}{2} e^\frac{i*3*\Theta}{2}$$ From here I mapped around a circle that was centered about the orgin. After cycling through 2 Pi I could see that z mapped into f(z) and wasn't at it's original point. So I concluded the branch points were at the origin and infinity (I think infinity is a branch point because z^-3/2 goes to 0 as z goes to infinity.

I think the cut can go from the origin to infinity in any direction.

The Riemann surfaces is giving me the most trouble. I keep going back and forth between this function being multivalued or not.

Thanks for any help!

2. Feb 19, 2016