Did you try setting up a system of partial differential equations?
From the Cauchy-Riemann equations, and . We have and . Try integrating and see what you get.
The exercise is as follows:
Harmonic function u is where a > 0 and z = x + iy in C. Find an analytic function f where f = u + v.
In the solution it is stated that since u and v are harmonic. I don't know how do deduce this.