(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 Hint: $z=(\sqrt{3}-3 \mathrm{i})^{n}=(-2 \sqrt{3})^{n}\left(-\frac{1}{2}+\frac{\sqrt{3}}{2} \mathrm{i}\right)^{n}, n=3$ is the smallest positive integer that makes $z$ a real number.