Proving the set of the $n$-th roots of unity form a cyclic subgroup

Question

All I recall about $\pi$, is that it is the torus and that it is a subgroup of $\mathbb C^\times$.

I read about the proof that forms a cyclic subgroup of $\mathbb C^\times$, but not sure about this one.

Answer 1

The complex numbers less $0$ are a group under multiplication. The roots inherit associativity, which is usually the hard one. You need to show closure and inverses.