 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ia/paper-1/8b/d/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Using

(a \cdot σ) (b \cdot σ) = (a \cdot b) I + i (a \times b) \cdot σ

gives

x' = x cos (2 θ) - (n \times x) sin (2 θ) + n (n \cdot x) (1 - cos (2 θ)) .

The sign follows from the convention

R = e^{i θ n \cdot σ}

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