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Math Help - Writing f(z) in its real and complex parts.

  1. #1
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    Writing f(z) in its real and complex parts.

    I need help rewriting f(z) as f(z)=u+iv. In particular I need help with sin(z^2) and sec(z).

    I believe Sec(z) would just be Sec(x)Sech(y)+i(-Csc(x)Csch(y)). Or just the inverse of cos(z)

    However I cannot find a way to relate Sin(z) to Sin(z^2).

    Thank You in advance.
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  2. #2
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    If you know sin(z)

    Why not just expand z^2 into real and imaginary parts, then it looks just like z' = (x^2 - y^2) + (2xy)i.

    Can you find sin(z^2) = sin(z') now?
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  3. #3
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    \sin(z^2)=\sin(x^2-y^2)\cosh(2xy)+i~\cos(x^2-y^2)\sinh(2xy)
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