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Math Help - Complex Analysis: Trig Functions

  1. #1
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    Complex Analysis: Trig Functions

    Find all solutions to:
    1) cosh(z)=-1-----done
    2) cos^2 (z)=4
    3) tan(z)=i
    Last edited by joestevens; October 27th 2010 at 04:01 PM. Reason: completed (1)
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Remember that

    \cos(z)=\frac{e^{iz}+e^{-iz}}{2}

    This gives

    \left(\frac{e^{iz}+e^{-iz}}{2} \right)^2=4 \iff e^{2iz}+2+e^{-2iz}=16

    (e^{2iz})^2-14e^{2iz}+1=0

    This is quadratic in e^{2iz}

    Can you finish from here?

    You will use a similar trick for tangent just write it as exponentials.
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  3. #3
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    I finished from there.

    Thanks.

    I got (3) to be no solution.
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