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Complex conjugate of a derivative wrt z

  1. May 11, 2012 #1
    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
     
  2. jcsd
  3. May 11, 2012 #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:
     
  4. May 11, 2012 #3
    Re: welcome to pf!

    That would be alright, because f*=z, so ∂(f*)/∂(z*) =0, so the formula works for this function
     
  5. May 11, 2012 #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:
     
  6. May 11, 2012 #5
    Thank you!
     
  7. May 12, 2012 #6
    I do not think this is correct.
     
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