Let $f(z)$ be an entire function, if $|f(z)| < \frac{1}{|Im z|}$ then f(z) must be constant.
I rewrote it as $|Im z||f(z)| <1$, then I defined $g(z) = Im z \cdot f(z) $, we know f(z) is entire, but unfortunately I can not say that about g(z) since Im z ist not even differentiable. How would be best to proceed here?
(I think in the end it must be proved that $f(z)$ is 0?)
