$12 \cdot 22$ Let the 20 vertices of a regular 20-sided polygon inscribed in the unit circle in the complex plane correspond to the complex numbers $z_{1}, z_{2}, \cdots, z_{20}$. 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.
(China High School Mathematics League, 1995)
［Solution］Let $z_{1}=\cos \theta+i \sin \theta$, then
$$
\begin{aligned}
z_{k}=(\cos \theta+i \sin \theta)\left[\cos \frac{2(k-1) \pi}{20}+i \sin \frac{2(k-1) \pi}{20}\right], \\
1 \leqslant k \leqslant 20 .
\end{aligned}
$$

From $1995=20 \times 99+15$, we get
$$
\begin{array}{l}
z_{k}^{1995}=(\cos 1995 \theta+i \sin 1995 \theta)\left(\cos \frac{3 \pi}{2}+i \sin \frac{3 \pi}{2}\right)^{k-1} \\
=(\cos 1995 \theta+i \sin 1995 \theta)(-i)^{k-1}, k=1,2, \cdots, 20 .
\end{array}
$$

Clearly, the above expression has four different values.
Therefore, the answer is $(A)$.