(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that every conformal self-map of the complex plane C has the form f(z) = az + b, where a ≠ 0. (Hint: The isolated singularity of f(z) at ∞ must be a simple pole.)

2. Relevant equations

3. The attempt at a solution

I know about conformal self-maps of the open unit disk, but this is about the complex plane. I don't know why the isolated singularity of f at ∞ must be a simple pole. I really don't know how I should start.

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# Conformal map

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