Find a function $u$ harmonic on $\{Im(z)>0, Re(z)>0\}$ with boundary values $0$ on $\{Im(z)>0, Re(z)=0\}$ and 1 on $\{Im(z) = 0, Re(z) > 0 \}$.
How does one go about this? My professor literally wrote:
"$u(z) = 1 - \frac{2}{\pi} Arg(z)$ works"
Any idea how to tackle this?