Answer to Question #231794 in Complex Analysis for Praise Johnwest

Question

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

Answer 1

For analyticity in a region $R$ of the $z$ -plane, $f$ must satisfy  Cauchy-Riemann equations relations

$$u_x=v_y, u_y=-v_x$$

at every point in that region.

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

Given: $u(x, y)$

Then

$$v=\int(-u_y)dx+\int u_xdy$$