# Find a conformal map from the exterior of the closed unit disk to the unit disk

Question: Find a conformal map from the exterior of the closed unit disk to the unit disk. Also, prove that it is indeed a conformal map (bijective and holomorphic along with its inverse).

I missed that the two days we covered conformal mapping due to chaos in my life. I have been trying to find worked out examples and have been reading up to get some insight, but I am lost since I can't find something that details a complete worked out problem.

p.s. If anyone knows a great resource that would help me out to further my grasp of conformal maps in complex analysis it'd be much appreciated if you could disclose this.

If you are working on $\mathbb{C}$, there is no such map (the exterior of the disc is not simply connected). If you're working on the Riemann sphere, investigate the mapping properties of $1/z$.
• $\bar{\mathbb{C}}$ is a common notation for the Riemann sphere – mrf Apr 15 '14 at 12:57