2003-9.md

course	course_year	question_number	tags	title	year
Complex Methods	IB	9	IB 2003 Complex Methods	1.II.16B	2003

Sketch the region $A$ which is the intersection of the discs

$$D_{0}={z \in \mathbb{C}:|z|<1} \quad \text { and } \quad D_{1}={z \in \mathbb{C}:|z-(1+i)|<1} .$$

Find a conformal mapping that maps $A$ onto the right half-plane $H={z \in \mathbb{C}: \operatorname{Re} z&gt;0}$. Also find a conformal mapping that maps $A$ onto $D_{0}$.

[Hint: You may find it useful to consider maps of the form $w(z)=\frac{a z+b}{c z+d}$.]