# Homework Help: Poles, zeroes, and essential singularities of z^(2/3)

1. Sep 7, 2008

### nathan12343

1. The problem statement, all variables and given/known data

Identify the zeroes, poles and essential singularities of $$f(z) = z^{2/3}$$

2. Relevant equations

$$f(z) = e^{\frac{2}{3}\log{z}}$$

Which I'm not sure will be useful....

3. The attempt at a solution

I know that f is 0 at $$z=0$$, but what is the order of this zero? Is there such a thing as a fractional order zero? Conversely, I know that there is a singularity at $$z=\infty$$, but this singularity seems to be a fractional order pole. Is this the case? I know that both of these points are also branch points, does that influence the problem at all?