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Complex conjugate of a derivative wrt z

by stallm
Tags: complex, conjugate, derivative
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stallm
#1
May11-12, 12:08 PM
P: 7
First post!

Is it true that for a complex function f([itex]{z}[/itex],[itex]\overline{z}[/itex])

[itex]\overline{\frac{∂f}{∂z}}[/itex] =[itex]\frac{∂\overline{f}}{∂\overline{z}}[/itex]

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
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tiny-tim
#2
May11-12, 01:32 PM
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hi stallm!welcome to pf!

but if f(z,z*) = z* then ∂f/∂z = 0
stallm
#3
May11-12, 01:52 PM
P: 7
Quote Quote by tiny-tim View Post
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

tiny-tim
#4
May11-12, 02:00 PM
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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*)*)
stallm
#5
May11-12, 02:08 PM
P: 7
Thank you!
jackmell
#6
May12-12, 07:54 AM
P: 1,666
Quote Quote by stallm View Post
First post!

Is it true that for a complex function f([itex]{z}[/itex],[itex]\overline{z}[/itex])

[itex]\overline{\frac{∂f}{∂z}}[/itex] =[itex]\frac{∂\overline{f}}{∂\overline{z}}[/itex]

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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