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Math Help - Hyperbolic functions

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    Hyperbolic functions

    Let z=x+iy. Verify that |sinhz|^2 = (sinhx)^2 + (siny)^2 and |coshz|^2 = (sinhx)^2 + (cosy)^2.

    Any suggestions?
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by paperclip View Post
    Let z=x+iy. Verify that |sinhz|^2 = (sinhx)^2 + (siny)^2 and |coshz|^2 = (sinhx)^2 + (cosy)^2.

    Any suggestions?
    This is plug and chug. \sinh(z)=\frac{e^{x+iy}-e^{-(x+iy)}}{2}. Go from there and remember that \left|z^2\right|=\left|z\right|^2
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