 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2005/ia/paper-1/5c/v/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

The cubic terms are the expansion of

(z + \overline{z})^{3} = (2 x)^{3}

. Subtracting

\overline{z} = x - i y

therefore gives

Re = 8 x^{3} - x, Im = y .

Here the expression is a polynomial in

z

and its complex conjugate, rather than a holomorphic polynomial in

z

alone.

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