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Math Help - Help with proving Complex variable equations

  1. #1
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    Help with proving Complex variable equations

    Hello, Could someone please Help with proving the Complex variable equation

    (a) If e^z E R. show that Im z = n \pi. where n E Z

    and if [TEX]e^z E i . R. then what is z =?

    Also, if someone knows of any book online or a resource that would help me with Basic Trancendental Functions chapter in complex variables, it will be GREATLY appreciated. The book that we have is completely useless
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  2. #2
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    Re: Help with proving Complex variable equations

    Quote Originally Posted by flametag2 View Post
    Hello, Could someone please Help with proving the Complex variable equation

    (a) If e^z E R. show that Im z = n \pi. where n E Z

    and if [TEX]e^z E i . R[COLOR=#444444][FONT=verdana]. then what is z =?
    You can use LaTeX code to make it more readable.
    [tex]e^{z}=e^{x}(\cos(y)+i\sin(y)[/tex] gives e^{z}=e^{x}(\cos(y)+i\sin(y)).

    You can see that is real only if y=n\pi where n\in\mathbb{Z}.

    I cannot read the second part of the question.
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