1. Let $z$ be a complex number, $\alpha(z)$ denote the smallest positive integer $n$ such that $z^{n}=1$. Then for the imaginary unit $\mathrm{i}, \alpha$ (i) $=$ ( ).
(A) 8
(B) 6
(C) 4
(D) 2
$-1, \mathrm{C}$.
Since $i^{1}=i, i^{2}=-1, i^{3}=-i, i^{4}=1$, therefore, the smallest positive integer $n$ that satisfies $z^{n}=1$ is $4$.