# Complex analysis zero/branch problem

1. Homework Statement

Let f be a holomorphic function in the open subset G or C. Let the point Z of G be a zero of f of order m. Prove that there is a branch of f^(1/m) in some open disk centered at Z

2. Homework Equations

Branch- a continuous function g in G such that, for each x in G, the value of g(x) is a value of f^(1/m)

3. The Attempt at a Solution

My biggest problem is formulating a proof that a branch exists. If somebody could give me a push start on how to start and formulate the proof that the branch exists I will be able to figure out the rest.