Let $\Omega$ be an open subset of C not containing $0$. Let $f$ be a complex valued continuous function on $\Omega$. Suppose $(f(z))^2=z^3$. Prove that f is holomorphic on $\Omega$.
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This has been asked and answered several times, for example http://math.stackexchange.com/questions/354249. (Also, please don't just copy a problem straight from your textbook. Tell us what you have tried, what tools you have available etc.) – mrf Feb 11 '14 at 20:40