Geometry of roots of unity

Question

Are they always equally-spaced on the unit circle, so that they always lie on the edges of equally-spaced wedges?

It seems like it, based on some sketching on paper, but if you can confirm or offer additional geometric information about these roots, please feel free.

Thanks,

Answer 1

The $n$th roots of unity are given by $e^{2\pi i j / n}$ where $0 \leq j < n$. These lie on the unit circle at angles $2\pi i j /n$, which are equally spaced with angles $2\pi i / n$ between subsequent roots.