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Complex analysis question

  • #1
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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???
 

Answers and Replies

  • #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!
 
  • #3
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so I took derivative and found x = 0 so does that mean C = 0 but I don't know how to get from here ?
 
  • #4
Office_Shredder
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so I took derivative and found x = 0 so does that mean C = 0 but I don't know how to get from here ?
I don't understand what you are saying here.
 
  • #5
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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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