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If f is analytic in $|z| \leq1 $ and satisfies $ |f(z)| = 1$ on $|z| = 1$ prove that f is a rational function. I need a clue how to think about this? should i use the fact that f can be written as a power series?

user333569
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    You can see this, it is a more general case : http://math.stackexchange.com/questions/783741/meromorphic-on-unit-disc-with-absolute-value-1-on-the-circle-is-a-rational-funct – Bérénice Apr 23 '16 at 20:46

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