Answer to Question #231794 in Complex Analysis for Praise Johnwest

Question #231794

Find a function v such that f(z) = u+iv is analytic [i.e. find the conjugate function of u ].

1
Expert's answer
2021-09-02T00:21:56-0400

For analyticity in a region RR of the zz -plane, ff must satisfy  Cauchy-Riemann equations relations


ux=vy,uy=vxu_x=v_y, u_y=-v_x

at every point in that region.

Let f(z)=u+ivf(z) = u + i v be an analytic function.

Given: u(x,y)u(x, y)

Then


v=(uy)dx+uxdyv=\int(-u_y)dx+\int u_xdy


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