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Math Help - Liouville's Theorem - advice needed please.

  1. #1
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    Liouville's Theorem - advice needed please.

    Could someone advise me how to use Liouville's Theorem to show that there is at least one value z0 in complex plain for which:

    |cos (zo/2009)| > 2009

    Thank you.
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  2. #2
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    Quote Originally Posted by grahamlee View Post
    Could someone advise me how to use Liouville's Theorem to show that there is at least one value z0 in complex plain for which:

    |cos (zo/2009)| > 2009

    Thank you.
    Consider the function f(z) = \cos \tfrac{z}{2009}. This is an entire function. If |f|\leq 2009 on the complex plane then f would be a constant function which it is not (by Louiville's theorem). Therefore, there has to exists at least one point z_0\in \mathbb{C} so that |f(z_0)| > 2009.
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    thank you so much
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