Let $G$ be a group. If we fix a $g\in G$, the cyclic subgroup $\langle g\rangle=\{g^n\mid n\in{\mathbb Z}\}$ of $G$ is, by definition, the subgroup of elements of the form $g^n$, as $n$ runs over all integers, and where $g\in G$ is fixed. We call $\langle g\rangle$ the cyclic subgroup of $G$ generated by $g$.

By definition, the group $G$ is cyclic if $G=\langle g\rangle$ for some $g\in G$. A cyclic group $C$ is called finite cyclic when its order $|C|$ is finite and infinite cyclic otherwise.

Which of the following are **TRUE**?

Here, $i=\sqrt{-1}$.

Select **ALL** that apply.