(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

[tex]f(z) = e^{\frac{2}{3}\log{z}}[/tex]

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

3. The attempt at a solution

I know that f is 0 at [tex]z=0[/tex], 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 [tex]z=\infty[/tex], 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?

Thanks for your help!

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**