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Math Help - Complex variable help

  1. #1
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    Complex variable help

    I am able to show that \mid (sin z)^2 \mid =  sin^2 x + sinh^2 x but I am a hard time trying to prove that the complex sine function is not bounded using this.

    could someone please help
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  2. #2
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    Re: Complex variable help

    Quote Originally Posted by flametag3 View Post
    I am able to show that \mid (sin z)^2 \mid =  sin^2 x + sinh^2 x but I am a hard time trying to prove that the complex sine function is not bounded using this.
    Have look at this plot. Is $\sinh^2(x)$ bounded?

    You should know that $|f^2(z)|=|f(z)|^2$
    So if $\sin(z)$ were bounded how does that yield a contradiction?
    Last edited by Plato; April 19th 2014 at 03:14 PM.
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