Hyperbolic distance in the Poincare half-plane

For

z, w

in the upper half-plane,

cosh d (z, w) = 1 + \frac{∣ z - w ∣ ^{2}}{2 Im z Im w} .

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Past exam of the mathematics course of the University of Cambridge / 2018 / ib / Paper 2 / 14G / b / Solution

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