Solving Harmonic Function: Find v(x,y) for u + iv Analytic on C

[squenshl]

Homework Statement

I have shown that u(x,y) = e^-xsin(y) is harmonic. That is u_xx+ u_yy = 0. How do I find a harmonic function v(x,y) such that u + iv is analytic on C.

Homework Equations

The Attempt at a Solution

I tried to find v(x,y) in the same fashion as you find a scalar potential, given a gradient but that was no go.
Would I find the Cauchy-Riemann equations & go from there?

 

[squenshl]

Never mind. Got it.
It was v(x,y) = e^-xcos(y) + K