Consider the set of $x$-th roots of unity. What is its cardinality?
Formally, consider $x \in \mathbb{C}$, and let
$S_x = \{y \in \mathbb{C} \; : \;$ there exist $k, m \in \mathbb{Z}$ such that $ x(\ln y + 2\pi i k) = 2\pi i m\} \}$.
This is based of multi-valued definition of $\ln$, as per a suggestion in the comments below. What is the cardinality of $S_x$?
For example, when $x = n \in \mathbb{Z}^+$, $S_n$ is just $n$. When $x=0$, the solutions are all $y \in \mathbb{C}$ except $y=0$.
What happens in other cases?