# Complex conjugate of a derivative wrt z

by stallm
Tags: complex, conjugate, derivative
 P: 7 First post! Is it true that for a complex function f(${z}$,$\overline{z}$) $\overline{\frac{∂f}{∂z}}$ =$\frac{∂\overline{f}}{∂\overline{z}}$ I think I proved this while trying to solve a problem. If it turns out it's not true and I've made a mistake, I'll upload my 'proof' and have the mistakes pointed out :) Thanks
 Sci Advisor HW Helper Thanks PF Gold P: 26,116 hi stallm!welcome to pf! but if f(z,z*) = z* then ∂f/∂z = 0
P: 7
 Quote by tiny-tim hi stallm!welcome to pf! but if f(z,z*) = z* then ∂f/∂z = 0
That would be alright, because f*=z, so ∂(f*)/∂(z*) =0, so the formula works for this function

HW Helper
Thanks
PF Gold
P: 26,116

## Complex conjugate of a derivative wrt z

 Quote by stallm First post! Is it true that for a complex function f(${z}$,$\overline{z}$) $\overline{\frac{∂f}{∂z}}$ =$\frac{∂\overline{f}}{∂\overline{z}}$ I think I proved this while trying to solve a problem. If it turns out it's not true and I've made a mistake, I'll upload my 'proof' and have the mistakes pointed out :) Thanks