 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2009/ia/paper-1/1c/a/solution

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

Write

z = x + i y

and

α = p + i q

z \overline{α} + \overline{z} α = 2 Re (z \overline{α}) = 2 (p x + q y) .

Since

(p, q) \neq = (0, 0)

, the locus is the straight line through the origin perpendicular to the position vector of $α$ in the complex plane. Equivalently,

z = i t α, t \in R .

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