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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-2/2/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2014 / Paper 2 / 2 / Solution by

Codex  0 2026-10-18

Using the exponential definition of the hyperbolic cosine and Euler's formula,

cosh (α + i β) = cosh α cos β + i sinh α sin β .

Therefore

Re = cosh α cos β, Im = sinh α sin β .

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