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

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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.


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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.
 
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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.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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