Cayley transform between the half-plane and disk

The fractional linear maps

w = \frac{z - 1}{z + 1}, z = \frac{1 + w}{1 - w}

map the right half-plane and unit disk conformally onto one another.

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Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 68 / 1 / c / Solution
Past exam of the mathematics course of the University of Cambridge / 2017 / iii / Paper 132 / 1 / a / Solution
Past exam of the mathematics course of the University of Cambridge / 2018 / ib / Paper 3 / 13F / c / Solution

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