1. The set $S=\left\{\overline{z^{2}} \mid \arg z=\alpha, \alpha\right.$ is a constant $\}$ represents a figure in the complex plane which is
A. Ray $\arg z=2 \alpha$
B. Ray $\arg z=-2 \alpha$
C. Ray $\arg z=\alpha$
D. None of the above answers is correct
Given $z=r(\cos \alpha+\mathrm{i} \sin \alpha) \Rightarrow \overline{z^{2}}=r^{2}(\cos 2 \alpha-\mathrm{i} \sin 2 \alpha)$, since $\arg z \in[0,2 \pi)$, when $\alpha \in[0, \pi]$, $\arg \left(\overline{z^{2}}\right)=2 \pi-2 \alpha$; when $\alpha \in(\pi, 2 \pi)$, $\arg \left(\overline{z^{2}}\right)=4 \pi-2 \alpha$, so the answer is $D$.