 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ia/paper-1/1c/iv/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

Factor the expression using the complex conjugate:

z^{3} - z^{2} \overline{z} - z \overline{z}^{2} + \overline{z}^{3} = (z + \overline{z}) (z - \overline{z})^{2} = (2 x) (2 i y)^{2} = - 8 x y^{2} .

It is real, so

Re = - 8 x y^{2}, Im = 0 .

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