2. In the complex plane, there are 7 points corresponding to the 7 roots of the equation $x^{7}=$ $-1+\sqrt{3} i$. Among the four quadrants where these 7 points are located, only 1 point is in ( ).
(A) the I quadrant
(B) the II quadrant
(C) the III quadrant
(D) the IV quadrant
2. (C).
$$
\begin{array}{l}
\because x^{7}=-1+\sqrt{3} \mathrm{i}=2\left(\cos 120^{\circ} + i \sin 120^{\circ}\right), \\
\therefore x_{n}=2^{\frac{1}{7}}\left(\cos \frac{\left(\frac{2}{3}+2 n\right) \pi}{7}+\sin \frac{\left(\frac{2}{3}+2 n\right) \pi}{7}\right) .
\end{array}
$$

where $n=0,1,2, \cdots, 6$.
After calculation, we get $\arg x_{0}=\frac{2 \pi}{21}, \arg x_{1}=\frac{8 \pi}{21}, \arg x_{2}=\frac{14 \pi}{21}$, $\arg x_{3}=\frac{20 \pi}{21}, \arg x_{4}=\frac{26 \pi}{21}, \arg x_{5}=\frac{32 \pi}{21}, \arg x_{6}=\frac{38 \pi}{21}$.
Clearly, there is only 1 root corresponding to a point in the third quadrant.