If I am given the function $\displaystyle u(x,y)$ wich could be the real part of an analytic complex function of complex variable, and $\displaystyle z=x+iy$, how can I compute a function $\displaystyle f(z)=u(x,y)+iv(x,y)$? I have to apply the Cauchy Riemann conditions ( $\displaystyle u_{x}=v_{y}$ and $\displaystyle u_{y}=-v_{x}$) and integrate both equations?

Thanks in advance