Analysis/Complex Analysis

[oab729]

Homework Statement

Show that for a polynomial of degree n, P(z), that for all z with |z| sufficiently large, there are positive constants c,d, s.t. c|z|^n < |P(z)| < d|z|^n

Homework Equations

The Attempt at a Solution

Assume it is true for n-1.
p(z)=az^n+q(z)
Then for z with sufficiently large |z|, there exist e,f s.t. e|z|^(n-1) < |q(z)| < f|z|^(n-1).

No idea how to continue.

 

[Billy Bob]

Try doing |P(z)| < d|z|^n and c|z|^n < |P(z)| as two different problems. Use triangle inequality. Try it with actual example polynomials first if you're still lost.