1. The set $S=\left\{\overline{z^{2}} \mid \arg z=a, a \in \mathbf{R}\right\}$ in the complex plane is represented by
(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
(D)
I. Multiple Choice Question
1.【Analysis and Solution】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, let $a=\frac{\pi}{6}$, then $\arg z=\frac{\pi}{6}$. As shown in the figure, it is the ray $O P_{0}$ on the complex plane.
$\arg z^{2}$ is the ray $O P_{1}$ in the figure, and $\overline{z^{2}}$ is symmetric to $z^{2}$ about the $O x$ axis, which is the ray $O P_{2}$. Clearly, $\arg \overline{z^{2}}=\frac{5 \pi}{3}$.
$\therefore$ The set $S=\left\{\overline{z^{2}} \left\lvert\, \arg z=\frac{\pi}{6}\right.\right\}$ is the ray $\arg z=\frac{5 \pi}{3}$ on the complex plane, thus eliminating (A), (B), and (C).