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 P: 26,148 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

 Sci Advisor HW Helper Thanks P: 26,148 Complex conjugate of a derivative wrt z ah, i misread it 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*)*)
 P: 7 Thank you!
P: 1,666
 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
I do not think this is correct.

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