复数 $z$ 满足 $|z|=9$ 且 $\frac12\pi\le\arg z\le\pi$。

(a) 在 Argand 图上，画出表示 $z$ 的点的轨迹的草图。

(b) 在同一幅图上，画出表示 $z^*+3$ 的点的轨迹的草图。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

模长固定给出圆，辐角限制选出第二象限的四分之一圆弧。两个端点都包括在内，不涂内部。

The locus lies on the circle with centre $O$ and radius $9$.

The restriction $\frac{\pi}{2}\leqslant\arg z\leqslant\pi$ selects the upper-left quarter of this circle, from $(0,9)$ to $(-9,0)$, including both endpoints.

Draw this arc only, with no shaded interior. The combined diagram for both parts is shown in (b).

先关于实轴反射，再沿实轴向右平移三个单位。两步都作用于整条圆弧及其端点。

Complex conjugation reflects the arc in the real axis. Adding $3$ then translates it $3$ units to the right.

Thus the new locus is the lower-left quarter of the circle with centre $(3,0)$ and radius $9$. Its endpoints are $(-6,0)$ and $(3,-9)$, both included.

Draw both arcs on the same Argand diagram, without shading either interior.