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**utopiaNow** Show that if $\displaystyle p_n(z) = a_nz^n + a_{n-1}z^{n-1} + \cdots + a_1z + 1$ is a polynomial of degree n with constant term 1, and if $\displaystyle |a_n| > 1$, then at least one of the roots of $\displaystyle p_n(z)$ lies inside the unit circle.

My attempt: The hint that's been given is to use the "factored form", which I assume means $\displaystyle p_n(z) = a_n(z - z_1)(z - z_2)\cdots(z - z_n)$.

But I'm not sure how to advance from here. Any suggestions would be appreciated as I'm literally stuck on the first step.

**Edit: Never mind, I solved it.**