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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???