Let $\alpha$ be a real number, $\mathrm{i}=\sqrt{-1}$, and let $a_{n}=\cos n \alpha+i \sin n \alpha$, then the sequence $\left\{a_{n} \mid(n \geqslant 1)\right.$ must be ( )
(A) an arithmetic sequence
(B) a geometric sequence with the modulus of the common ratio being 1
(C) a non-constant geometric sequence
(D) a geometric sequence with the modulus of the common ratio greater than 1
2. (B). 
$\cos n \alpha+\mathrm{i} \sin n \alpha=(\cos \alpha+\mathrm{i} \sin \alpha)^{n}$, note $|\cos \alpha+\mathrm{i} \sin \alpha|=1$.