Show that the function $\phi(x, y)=\tan ^{-1} \frac{y}{x}$ is harmonic. Find its harmonic conjugate $\psi(x, y)$ and the analytic function $f(z)$ whose real part is $\phi(x, y)$. Sketch the curves $\phi(x, y)=C$ and $\psi(x, y)=K$.