There are 24 different complex numbers $z$ such that $z^{24}=1$. Then the number of $z$ such that $z

Question

There are 24 different complex numbers $z$ such that $z^{24}=1$. Then the number of $z$ such that $z^6$ is real is

Professor PC Thomas Classes · Answer

Roots of unity $z^{24}=1$. To have $z^6$ real, $z$ must be a multiple of $\frac{\pi}{6}$ roots, totaling 12 values.