Let $n$ be a positive integer. Prove that if $z\_1$ is any $n$-root of $z$, that is, $z\_1^n=z$, then, $z\_1,z\_1\omega, \dotsc, z\_1\omega^{n-1}$ are the $n$-roots $n$-th of $z$ where $\omega = \cos(2\pi/n)+i\sin(2\pi/n)$.