f and g are entire and $ \left|f(z)\right| \leq \left|g(z)\right| $ then $\exists \alpha\in \mathbb{C}$ such that $f(z)=\alpha g(z)$
Suppose $f$ and $g$ are entire functions, and $|f(z)| \leq |g(z)|$ for all $z \in \mathbb{C}$, Prove that $f(z)=cg(z)$.