Is $$ \bigcup\_{n=1}^{\infty}\{z\in\Bbb C:z^n=1\}=\{z\in\Bbb C:|z|=1\}$$my argument is that the argument of the elements of the first set are rational multiples of $\pi$ whereas the second set also consists of elements with irrational multiples of $\pi$.
But I am not so sure, there is still some doubt.