4. The 7 roots of the equation $z^{7}=-1+\sqrt{3} i$ correspond to 7 points on the complex plane. Among the four quadrants, the quadrant that contains only 1 point is ( ).
A. First Quadrant
B. Second Quadrant
C. Third Quadrant
D. Fourth Quadrant
4. C

Since $z^{7}=2\left(\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}\right)$, by the root extraction of complex numbers, the 7 roots are $\varepsilon_{k}=7 \sqrt{2}\left(\cos \theta_{k}+i \sin \theta_{k}\right)$, where $\theta_{k}=\frac{2 k \pi+\frac{2 \pi}{3}}{7}, k=0,1,2, \cdots, 6$. It is easy to find that $\theta_{0}=\frac{2 \pi}{21}, \theta_{1}=\frac{8 \pi}{21}, \theta_{2}=\frac{2 \pi}{3}, \theta_{3}=\frac{20 \pi}{21} . \theta_{4}=\frac{26 \pi}{21}, \theta_{5}=\frac{32}{21} \pi, \theta_{6}=\frac{38}{21}$ $\pi$, so only $\theta_{4}$ is the angle in the 3rd quadrant.