# Does the principal branch square root of z have a Laurent series expansion C-{0}?

## Homework Statement

Does the principal branch square root of z have a Laurent series expansion in the domain C-{0}?

## The Attempt at a Solution

Well I'm not really sure what a principal branch is? I believe that there is a Laurent series expansion for z^(1/2) in C-{0} because originally our only problem is that when we take derivative of z^1/2 we get 1/z^[(2n+1)/2] and this is not defined at 0, but is everywhere else... so I think the answer is yes to this, but again I'm unsure of the details of principal branch?