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Math Help - Complex Variable help

  1. #1
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    Complex Variable help

    Could someone help me and explain how to write teh following in terms of x and y. I have seen some examples but I dont seem to be able to do this one on my own.


    |e^{5z+3i+2}| and |e^{iz^2}|

    and show that |e^{5z+3i+2} + e^{iz^2}| \not\leq e^{5x + 2} + e^{-2xy}
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  2. #2
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    Re: Complex Variable help

    Quote Originally Posted by flametag2 View Post
    Could someone help me and explain how to write teh following in terms of x and y. I have seen some examples but I dont seem to be able to do this one on my own.


    |e^{5z+3i+2}| and |e^{iz^2}|
    What are you supposed to do with these? You should know that |e^{ia}| is equal to 1 for any a.
    Amd |e^{5z+ 3i+ 2}|= |e^{5z}||e^{3i}||e^2|. And, again, |e^{3i}|= 1.

    and show that |e^{5z+3i+2} + e^{iz^2}| \not\leq e^{5x + 2} + e^{-2xy}
    Are we to assume here that z= x+ iy?
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  3. #3
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    Re: Complex Variable help

    Quote Originally Posted by flametag2 View Post
    Could someone help me and explain how to write teh following in terms of x and y. I have seen some examples but I dont seem to be able to do this one on my own.
    |e^{5z+3i+2}| and |e^{iz^2}|
    and show that |e^{5z+3i+2} + e^{iz^2}| \not\leq e^{5x + 2} + e^{-2xy}
    Where did you find this question?

    It is easy to show that \left|e^z\right|=e^{\text{Re}(z)}.

    Because |z+w|\le |z|+|w| for all complex z~\&~w, how can the inequality not hold?
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