Using Liouville's Theorem to Show f is Constant

[smoothman]

Suppose f is an entire function such that $f(z) = f(z+2\pi)$
and $f(z)=f(z+2\pi i)$ for all z $\epsilon$ C. How can you use Liouville's theorem to show f is constant..

any help on that please to get me started off.. thnx a lot :)

 

[Xevarion]

The two given relations tell you that $$f$$ is completely determined by its values in a square of side length $$2\pi$$... what do you need to show about $$f$$ to use Liouville? Can you get it from this info now?

 

[mathwonk]

not just completely determined, but actually that it maps that square onto its range of values.