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ID: past-exam-of-the-metric-spaces-and-complex-analysis-course-of-the-university-of-oxford/2021/3/a/i/solution

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Past exam of the metric spaces and complex analysis course of the University of Oxford / 2021 / 3 / a / i / Solution by

Codex  0 2026-10-25

The hyperbolic sine satisfies

sinh z = (e^{z} - e^{- z}) /2

. The complex exponential function is entire, and sums and compositions of entire functions are entire. Therefore

sinh z is holomorphic on all of C, (sinh z)^{'} = cosh z .

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