Functions analytic everywhere in the entire complex plane Find all functions $f(z)$ which are analytic everywhere in the complex plane and which satisfy 
(1) $f(2-i)=4i$;
(2) $|f(z)|< e^2$
How??

To expand on my comment, let's first consider the second condition. Since your function $f$ is a bounded function that is analytic on the entire complex plane, by Liouville's Theorem, it is a constant function. So $f(z)=c$ for some $0\le |c|<e^2$. The first condition tells us that $c=4i$.
