2007-35.md

course	course_year	question_number	tags	title	year
Complex Methods	IB	35	IB 2007 Complex Methods	$3 . \mathrm{I} . 5 \mathrm{~F} \quad$	2007

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 $\psi(x, y)=K$.