Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / 7 / i / Solution

The complex potential of a two-dimensional potential flow combines the velocity potential $u$ with the stream function $v$. For its holomorphic representation, the Cauchy-Riemann equations are $u_x=v_y$ and $u_y=-v_x$.