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Math Help - how to show this complex function not differentiable

  1. #1
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    how to show this complex function not differentiable

     f(z)=\frac{z^{5}}{|z|^{4}} , f(0)=0

    Show the real and imaginary parts of f satisfy the Cauchy-Riemann, and f is not differentiable.

    i show the first part, but i think if Cauchy-Riemann is satisfied, then f is differentiable?
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  2. #2
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    Quote Originally Posted by szpengchao View Post
     f(z)=\frac{z^{5}}{|z|^{4}} , f(0)=0

    Show the real and imaginary parts of f satisfy the Cauchy-Riemann, and f is not differentiable.

    i show the first part, but i think if Cauchy-Riemann is satisfied, then f is differentiable?
    If the Cauchy-Riemann equations are satisfied and f has continuous first order partial derivatives, then f is differentiable.

    The C-R equations alone are not enough.
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