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Analysis/Complex Analysis

  1. Apr 16, 2009 #1
    1. The problem statement, all variables and given/known data
    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


    2. Relevant equations



    3. 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.
     
  2. jcsd
  3. Apr 17, 2009 #2
    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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