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Math Help - [SOLVED] Complex function proof

  1. #1
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    [SOLVED] Complex function proof

    Show that neither sin(\bar{z}) nor cos(\bar{z}) is an analytic function of z anywhere.

    Is it sufficient to say that neither function is analytic because neither can be put into the form f(z)=u(x,y)+iv(x,y) and therefore they can't possibly satisfy the Cauchy-Riemann equations anywhere?
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    \sin\left(\overline{z}\right)=\\sin(x)\cosh(-y)+i\cos(x)\sinh(-y)
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    I've not seen that identiy for sin(z) before, but I ended up deriving it in the meantime. Is there a list of similar identities somewhere?
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    Quote Originally Posted by davesface View Post
    I've not seen that identiy for sin(z) before. Is there a list of similar identities somewhere?
    Any cpmplex variables textbook should have such a list.
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