# Math Help - how to show this complex function not differentiable

1. ## 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?

2. 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.