2005-31.md

course	course_year	question_number	tags	title	year
Complex Analysis or Complex Methods	IB	31	IB 2005 Complex Analysis or Complex Methods	1.II.13F	2005

Determine a conformal mapping from $\Omega_{0}=\mathbf{C} \backslash[-1,1]$ to the complex unit disc $\Omega_{1}={z \in \mathbf{C}:|z|<1} .$

[Hint: A standard method is first to map $\Omega_{0}$ to $\mathbf{C} \backslash(-\infty, 0]$, then to the complex right half-plane ${z \in \mathbf{C}: \operatorname{Re} z>0}$ and, finally, to $\left.\Omega_{1} .\right]$