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