We fix an integer $n \geq 1$ and $A(z) = \sum_{k=0}^{n-1} a_k z^k$ a polynomial such that $a_k \in \{-1, 0, 1\}$ for all $0 \leq k \leq n-1$. If $z \in \mathbb{C}$ satisfies $|z| = 1$, show that $|A(z)| \leq n$.
We fix an integer $n \geq 1$ and $A(z) = \sum_{k=0}^{n-1} a_k z^k$ a polynomial such that $a_k \in \{-1, 0, 1\}$ for all $0 \leq k \leq n-1$. If $z \in \mathbb{C}$ satisfies $|z| = 1$, show that $|A(z)| \leq n$.