Analysis/Complex Analysis

  • Thread starter oab729
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  • #1
oab729
12
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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.
 

Answers and Replies

  • #2
Billy Bob
392
0
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.
 

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