1. The set $S=\left\{\overline{Z^{2}} \mid \arg Z=a, \dot{a}\right.$ is a constant $\}$ in the complex plane is
(A) ray $\arg Z=2 a$;
(B) ray $\arg Z=-2 a$;
(C) ray $\arg Z=-a$;
(D) none of the above answers is correct.
1. (D)

According to the definition of the principal value of the argument of a complex number in high school general textbooks, $0 \leqslant \arg z < 2 \pi$.
Using the method of special values to eliminate options,
let $\alpha=\frac{\pi}{6}$,
then $\arg z=\frac{\pi}{6}$,

The figure shows the ray $O P_{0}$ in the complex plane.
$\arg z^{2}$ is the ray $O P_{1} \overline{z^{2}}$ in the figure, and $z^{2}$ is symmetric to $\overline{z^{2}}$ about the $o x$ axis as the ray $O P_{2}$. Clearly, $\arg \overline{z^{2}}=\frac{5 \pi}{3}$.
$\therefore$ The set $S=\left\{\overline{z^{2}} \left\lvert\, \arg z=\frac{\pi}{6}\right.\right\}$ in the complex plane is the ray $\arg z =\frac{5 \pi}{3}$, thus eliminating $(\mathrm{A}) 、(\mathrm{~B}) 、(\mathrm{C})$.