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## Homework Statement

Suppose p is a polynomial of degree n and |p(z)|≤M if |z|=1

Show that |p(z)|≤M|z|[itex]^{n}[/itex] if |z|≥1

## Homework Equations

Maximum Modulus Principle: If f is a nonconstant analytic function on a domain D, then |f| can have no local maximum on D.

## The Attempt at a Solution

Book says to apply the maximum modulus principle to [itex]\frac{p(z)}{z^{n}}[/itex] on domain |z|>1 but I am unsure why?