2. Let the 20 vertices of a regular 20-sided polygon inscribed in the unit circle in the complex plane correspond to the complex numbers $Z_{1}, Z_{2}, \cdots, Z_{20}$, respectively. Then the number of different points corresponding to the complex numbers $Z_{1}^{1995}, Z_{2}^{1995}, \cdots, Z_{20}^{1995}$ is
(A) 4
(B) 5
(C) 10
(D) 20
(A)
2. 【Analysis and Solution】Solution 1
Let $Z_{1}=\cos \theta+i \sin \theta$, then
$$
Z_{k}=(\cos \theta+i \sin \theta)\left(\cos \frac{2(k-1) \pi}{20}\right)+i \sin \frac{2(k-1) \pi}{20}, 1 \leqslant k \leqslant 20
$$

From $1995=20 \times 99+15$, we get
$$
\begin{aligned}
Z_{k}^{1905} & =(\cos 1995 \theta+i \sin 1995 \theta)\left(\cos \frac{3 \pi}{2}+i \sin \frac{3 \pi}{2}\right)^{k-1} \\
& =(\cos 1995 \theta+i \sin 1995 \theta)(-i)^{k-1}, k=1,2, \cdots, 20 \text {, there are four different values, hence choose (A). }
\end{aligned}
$$

Solution 2
Assume $Z_{1}, Z_{2}, \cdots, Z_{20}$ are the 20 20th roots of unity, then $Z_{1}^{1995}, Z_{2}^{1095}, \cdots, Z_{20}^{1905}$ must be the 4th roots of unity, and it is not difficult to see that $Z_{1}^{1995}, Z_{2}^{1995}, \cdots, Z_{20}^{1995}$ include the 4 4th roots of unity, hence the number of different points corresponding to $Z_{1}^{1995}, Z_{2}^{1995}, \cdots, Z_{20}^{1995}$ is 4.