= 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 gives
$$
\overline{\frac{m}{-i\bar z-a}}=\frac{\bar m}{iz-\bar a}=-\frac{i\bar m}{z+i\bar a}.
$$
Consequently
$$
\boxed{W(z)=\frac{m}{z-a}-\frac{i\bar m}{z+i\bar a}}.
$$
The image lies at $-i\bar a$, with moment $-i\bar m$, on the opposite side of the wall.
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