# how to show this complex function not differentiable

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• January 30th 2009, 04:28 AM
szpengchao
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?
• January 30th 2009, 05:45 PM
awkward
Quote:

Originally Posted by szpengchao
$f(z)=\frac{z^{5}}{|z|^{4}} , f(0)=0$

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.