Proof with Complex Variables

Let f(z) be entire and let |f(z)| ≥ 1 on the whole complex plane. Prove that f
is constant

Just consider 1 / f(z), and use Liouville's theorem.

-----

"I tried Liouville's thereom but that only applies when f(z) <= M"

Hrmmm? That's why you need to consider 1 / f(z) instead of f(z)...