1. In the complex plane, the vector corresponding to the complex number $3-\sqrt{3} i$ is rotated clockwise by $\frac{\pi}{3}$. The complex number corresponding to the resulting vector is
A. $2 \sqrt{3}$
B. $-2 \sqrt{3} \mathrm{i}$
C. $\sqrt{3}-3 \mathrm{i}$
D. $3+\sqrt{3} \mathrm{i}$
1. B $\frac{3-\sqrt{3} i}{\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}}=(3-\sqrt{3} i)\left(\cos \frac{\pi}{3}-i \sin \frac{\pi}{3}\right)=(3-\sqrt{3} i)\left(\frac{1}{2}-\frac{\sqrt{3}}{2} i\right)=-2 \sqrt{3} i$