Past exam of the mathematical methods I course of the University of Oxford / 2022 / 9 / a / i

The right-hand side has modulus two and argument $\pi /3$. Its fifth roots therefore haveThey are the vertices of a regular pentagon on the circle of radius $2^{1/5}$, beginning at angle $\pi /15$. These five roots are distinct, and a degree-five polynomial has no further complex roots.