- #1

Crush1986

- 207

- 10

## Homework Statement

[tex] f(z)=z^\frac{3}{2} [/tex] find the branch points, branch cuts, and Riemann sheet structure.

## Homework Equations

none

## The Attempt at a Solution

So, I converted this to complex exponential form [tex] r^\frac{3}{2} e^\frac{i*3*\Theta}{2} [/tex] 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!