Complex conjugate of a derivative wrt z

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  • #1
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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
 

Answers and Replies

  • #2
tiny-tim
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welcome to pf!

hi stallm!welcome to pf! :smile:

but if f(z,z*) = z* then ∂f/∂z = 0 :confused:
 
  • #3
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hi stallm!welcome to pf! :smile:

but if f(z,z*) = z* then ∂f/∂z = 0 :confused:
That would be alright, because f*=z, so ∂(f*)/∂(z*) =0, so the formula works for this function
 
  • #4
tiny-tim
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ah, i misread it :redface:

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*)*) :smile:
 
  • #5
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Thank you!
 
  • #6
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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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