1. The set $S=\left\{\overline{z^{2}} \mid \arg z=a, a\right.$ 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
$$
\arg z=\frac{\pi}{6},
$$

as shown in the ray $O P_{0}$ on the complex plane.
$\arg z^{2}$ is the ray $O P_{1} \bar{z}^{2}$ and
$z^{2}$ is symmetric to $O x$ as the ray $O P_{2}$, clearly
$$
\arg \bar{z}^{2}=\frac{5 \pi}{3}
$$
$\therefore$ The set $S=\left\{\bar{z}^{2} \left\lvert\, \arg z=\frac{\pi}{6}\right.\right\}$ in the complex plane is the ray $\arg z=\frac{5 \pi}{3}$, thus eliminating (A), (B), (C).