Complex Analysis Liouville's Theorem

Question

I am not sure how to solve the following problem:

Use Liouville's theorem to prove that if f(z) is holomorhpic in the in entire complex plane and $f(z+1) = f(z)$, and $f(z+i)=f(z)$ for all $z$ in $C$ then $f$ is constant.

I have never done a Liouville's theorem question before - is there a general method to doing these types of questions?

Thanks

You may want to provide a reference to Liouville's theorem to make it easier for someone wanting to help you out. — Jonas Dahlbæk, Aug 18 '14 at 17:17

score 1 · Answer 1 · answered Aug 18 '14 at 17:16

1

Hint:Show that $f$ is bounded, using the two periods $1$ and $i$.

answered Aug 18 '14 at 17:16

Hamou

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Complex Analysis Liouville's Theorem

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