If $|p(z)| \leq 1$ for all $z$ with $|z| \leq 1$, then show that $p(z)=z^n, \forall z\in \mathbb{C}$
Let $p(z)=z^n+a_{n-1}z^{n-1}+a_{n-2}z^{n-2}+...+a_0$ be a complex polynomial satisfying $|p(z)| \leq 1$ for $|z|\leq 1$, then prove that $p(z)=z^n$