2. Given $z=(\sqrt{3}-3 \mathrm{i})^{n}$. If $z$ is a real number, then the smallest positive integer $n$ is ().
(A) 3
(B) 4
(C) 5
(D) 6
2. A.

Notice,
$$
\begin{array}{l}
z=(\sqrt{3}-3 \mathrm{i})^{n} \\
=(-2 \sqrt{3})^{n}\left(-\frac{1}{2}+\frac{\sqrt{3}}{2} \mathrm{i}\right)^{n} .
\end{array}
$$

Therefore, $n=3$ is the smallest positive integer that makes $z$ a real number.