prove the the conjugate of a holomorphic function f is differentiable iff f'=0

This probably has a simple solution, but I cannot find it so far...

Quote:

Originally Posted by **problem statement**

Suppose the complex-valued function

is holomorphic about zero. Show that

, i.e. the conjugate of

, is differentiable at

if and only if

.

The first direction follows fairly directly from the Cauchy-Riemann equations. However, I still need to show that implies exists, and I can't seem to make it happen. Any help would be much appreciated.

Thanks!