MathNet 2026 — Part 09 Question 150

Let $0 \lt a_{0} \leq a_{1} \leq \cdots \leq a_{n}$. If $z$ is a complex number such that $a_{0} z^{n} + a_{1} z^{n-1} + \cdots + a_{n} = 0$ prove that $|z| \geq 1$.