# Complex conjugate of a derivative wrt z

1. May 11, 2012

### 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

2. May 11, 2012

### tiny-tim

welcome to pf!

hi stallm!welcome to pf!

but if f(z,z*) = z* then ∂f/∂z = 0

3. May 11, 2012

### stallm

Re: welcome to pf!

That would be alright, because f*=z, so ∂(f*)/∂(z*) =0, so the formula works for this function

4. May 11, 2012

### tiny-tim

in that case, yes …

it's f(x,y), you're swapping x and y, differentiating wrt x instead of y, and swapping back again (for ∂f/∂z = (∂f*/∂z*)*)

5. May 11, 2012

### stallm

Thank you!

6. May 12, 2012

### jackmell

I do not think this is correct.