Past exam of the options II course of the University of Oxford / 2008 printed variant / K / K3 / c / Solution

Reflection in the line $y=-x$ is $Rz=\overline{iz}=-i\bar{z}$. The printed expression has two conjugation bars: $w(z)+\overline{w(\overline{iz})}$. On the line $Rz=z$, this is $w(z)+\overline{w(z)}$, which is real; hence its stream function vanishes there. Applying this reflection to the dipole givesConsequentlyThe image lies at $-i\bar{a}$, with moment $-i\bar{m}$, on the opposite side of the wall.