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Math Help - Bounded polynomials.

  1. #1
    Ant
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    Bounded polynomials.

    Hi,

    if  f(z) is a polynomial with z a complex number. Then, is it always true that if the domain of f is bounded then f must be a bounded function?

    Also, is it aways true that as we increase |z| we see that |f(z)| increase also? I think this must be the case as polynomials only admit non negative powers.

    any help or clarification would be appreciate!

    Thanks
    Last edited by Ant; March 25th 2013 at 12:07 PM.
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  2. #2
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    Re: Bounded polynomials.

    1. Yes. |f(z)| = |an z^n +...+ a0 | <= |an||z|^n + ... + |a0|
    2. When |z| is big enough this is true. While if z is relatively small consider the example f(z)=1-z. |f(1)|=0<1=|f(0)|
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