Hello, I have a basic (I think) question about Roots of Unity. First I feel like I should mention that I have only the most basic understanding of complex numbers. Here is what I have been asked to prove:

An $\displaystyle n$th root of unity is a complex number $\displaystyle z$ such that $\displaystyle z^{n}=1$. Prove that the $\displaystyle n$th roots of unity form a cyclic subgroup of $\displaystyle \mathbb{C}^{\times}$ of order $\displaystyle n$.

This is my first exposure to roots of unity, but after looking through a number theory book, I feel like the first sentence should include "...where $\displaystyle n\in\mathbb{Z}^{+}$. Am I right about this?

If I am correct about this then how do I prove that each $\displaystyle n$th root of unity has an inverse?

Then, how do I express the identity element of $\displaystyle \mathbb{C}^{\times}$?

I am feeling pretty lost here. Thanks in advance.