 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-4/40e/d/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Here

ω_{4} = i

. Splitting into even and odd pairs gives

y^{(E)} = (1, 1), y^{(O)} = (- 1, - 1),

(2, 0)

and

(- 2, 0)

. The butterfly therefore yields

F_{4}^{- 1} (1, - 1, 1, - 1) = (0, 0, 4, 0) .

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