2016-7.md

course	course_year	question_number	tags	title	year
Complex Analysis	IB	7	IB 2016 Complex Analysis	Paper 4, Section I, G	2016

State carefully Rouché's theorem. Use it to show that the function $z^{4}+3+e^{i z}$ has exactly one zero $z=z_{0}$ in the quadrant

$${z \in \mathbb{C} \mid 0<\arg (z)<\pi / 2}$$

and that $\left|z_{0}\right| \leqslant \sqrt{2}$.