Complex velocity
= Complex velocity
{title2=$q=W'=u-iv$}
For a <complex potential of a two-dimensional potential flow> $W=\phi+i\psi$ in the coordinate $z=x+iy$, the <Cauchy-Riemann equations> give $W'=\phi_x-i\phi_y=u-iv$. A material point with physical <velocity> $(u,v)$ therefore satisfies $\dot z=\overline{W'(z)}$. Complex conjugation matters when deriving a <pathline> from a <complex potential of a two-dimensional potential flow>.