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 $\mathrm{i}, \alpha(\mathrm{i})=(\quad$.
(A) 8
(B) 6
(C) 4
(D) 2
1 $\mathrm{C}$ Hint: Since $\mathrm{i}^{1}=\mathrm{i}, \mathrm{i}^{2}=-1, \mathrm{i}^{3}=-\mathrm{i}, \mathrm{i}^{4}=1$, the smallest positive integer $n$ that satisfies $z^{n}=1$ is 4. Therefore, the answer is C.