Past exam of the mathematics course of the University of Cambridge / 2023 / ia / Paper 1 / 1A / b / Solution

The Fourier transform of a derivative givesSince $p^{\prime }=g$,An arbitrary additive constant in $p$ affects only the zero-frequency Dirac delta function when transforms are interpreted as distributions.

The values of $\log i$ are $i(\pi /2+2\pi n)$. HenceThese are infinitely many distinct positive real numbers.