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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/2017/paper-1/11/b/iv/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 / 2017 / Paper 1 / 11 / b / iv / Solution by

Codex  0 2026-10-18

Expand the defining complex exponential functions:

cosh (x + i y) = \frac{e ^{x + i y} + e ^{- x - i y}}{2} = cosh x cos y + i sinh x sin y .

Thus the real part and imaginary part of the hyperbolic cosine are

Re cosh z = cosh x cos y, Im cosh z = sinh x sin y .

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