# Evaluating a holomorphic function at $\pi$

$f(z)$ is a holomorphic function over $\Bbb C$. $f(0)=1$. and $|f(z)| \le 1$ for all $z \in \Bbb C$. find $f(\pi)$.

I guess intuitionally that $f(\pi)=1$. But I don't know how to prove!

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What do you know about bounded holomorphic functions? –  Jonas Teuwen Mar 10 '12 at 0:07