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Math Help - Showing that f'(z) does not exist at any point (complex analysis)

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    Showing that f'(z) does not exist at any point (complex analysis)

    I am having a hard time showing that f'(z) does not exist at any point for

    f(z)=z-z(conjugate)

    An explanation would be greatly appreciated,

    Thanks.
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    Quote Originally Posted by nankor View Post
    I am having a hard time showing that f'(z) does not exist at any point for

    f(z)=z-z(conjugate)

    An explanation would be greatly appreciated,

    Thanks.
    do you mean

    f(z)=z-\bar z=x+iy-(x-iy)=2yi

    so u(x,y)=0 \mbox{ and } v(x,y)=2y

    \frac{\partial u }{\partial x} =0

    \frac{\partial v}{\partial y}=2

    So f(z) does not satisfy the cauchy-reimann equation at any point so it is not diff at any point
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