HMMT 2021 U29

Compute the number of complex numbers $z$ with $|z|=1$ that satisfy

$1+z^{5}+z^{10}+z^{15}+z^{18}+z^{21}+z^{24}+z^{27}=0$

Dataset text NuminaMath olympiads. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.