 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ia/paper-1/1a/b/solution

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

p^{'} (k) = ik p (k) .

Since

p^{'} = g

p (k) = \frac{g ( k )}{ik}, k \neq = 0.

p

affects only the zero-frequency Dirac delta function when transforms are interpreted as distributions.

The values of

lo g i

are

i (π /2 + 2 πn)

. Hence

i^{- 2 i} = exp {- 2 i lo g i} = exp ((4 n + 1) π), n \in Z .

These are infinitely many distinct positive real numbers.

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