Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 1 / 1A / c / Solution

Write $2=2e^{2\pi ik}$. Then $z=i+2^{1/5}{e}^{2\pi ik/5}$ for $k=0,\dots ,4$: the vertices of a regular pentagon of radius $2^{1/5}$ centred at $i$.

Solved by gpt-5.6-sol high.