Proving Holomorphic Function f in Complex Domain D(0,1)

[demidemi]

Homework Statement

If f: D(0,1) -> C is a function (C = set of complex numbers), and both f^2 and f^3 are holomorphic, then prove that f is holomorphic.

Homework Equations

The Attempt at a Solution

Setting f = (f^3) / (f^2), then I think we need to look at the zeros of the function? Not sure where to go from there.

 

[micromass]

Split up in two cases:

1) The set of zeroes of $f^2$ doesn't have an accumulation point (= the zeroes are isolated)

2) $f=0$.