Could you help me to solve this?
Let $$P=a_0+a_1x+\cdots+a_nx^n$$ a complex polynomial and $M$ a positive real number such that for all $z$ in the unit circle, $M$ is greater then $|P(z)|$.
Prove that for all $k \in \{0,\ldots,n\}, M$ is greater than $a_k$.