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Complex analysis question

  1. Oct 8, 2013 #1
    Find the harmonic conjugate of u. u = u(z) = ln(|z|) so u(z) = ln(sqrt(x^2 + y^2))

    so basically I am trying to find now its harmonic conjugate I did all the math

    I got two solutions though one is v(z) = arctan(y/x) + C if I solve Au/Ax = -Au/Ay & other is
    v(z) = - arctan(x/y) + C if I solved Av/Ay = Au/ax
    so I was wondering can I ave two solutions or wat ? or is one solution more right than other???
     
  2. jcsd
  3. Oct 8, 2013 #2

    Office_Shredder

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    It might help to know that [itex] \arctan(x) + \arctan(1/x) [/itex] is locally a constant. Try taking the derivative!
     
  4. Oct 8, 2013 #3
    so I took derivative and found x = 0 so does that mean C = 0 but I don't know how to get from here ?
     
  5. Oct 8, 2013 #4

    Office_Shredder

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    I don't understand what you are saying here.
     
  6. Oct 8, 2013 #5
    I tried first to see arctan(x) + arctan(x^-1) to see if its a local constant on wolf ram alpha I didn't see any I don't understand how can that help.
     
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