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Complex polynomial

  1. Mar 7, 2008 #1
    If p(z)=a0+a1z+...+anz^n, and max|p(z)|=M for |z|=1, show that each coefficient ak is bounded by M.

    I'm trying to take derivatives but it's not getting anywhere. Thanks!
  2. jcsd
  3. Mar 7, 2008 #2
    Did you replace z with:

    [tex]exp(i \theta)[/tex]

    I suppose differentiating with respect to theata would make sence:

    This would give you:

    [tex]\sum_0^Na_n(-i)^n exp(-i n \theta)=\sum_0^Na_n exp(i n (\theta+\pi/2))=\sum_0^Na_n (i Z)^n[/tex]

    Yeah, I'm stuck to.
    Last edited: Mar 7, 2008
  4. Mar 7, 2008 #3


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    does cauchy's formula help?
    Last edited: Mar 7, 2008
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