在 Argand 图上用阴影标出一个区域，使其中的点表示同时满足不等式 $|z-3\mathrm{i}|\le2$ 和 $\frac14\pi\le\arg(z-1-2\mathrm{i})\le\frac34\pi$ 的复数 $z$。

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。

先画圆盘，再以平移后的点为顶点画辐角扇形。辐角在顶点没有定义，因此即使两条射线包括边界，顶点本身仍应排除。

The inequality $|z-3\mathrm{i}|\leqslant2$ represents the closed disk with centre $(0,3)$ and radius $2$.

The argument is measured from $P=(1,2)$, since $z-1-2\mathrm{i}=z-(1+2\mathrm{i})$. Draw rays from $P$ at angles $\pi/4$ and $3\pi/4$ to the positive real direction.

Writing $z=x+y\mathrm{i}$, the sector is

Shade the intersection of this upward sector with the disk. Include the circular and ray boundaries where defined, but mark $P$ as excluded because $\arg0$ is undefined.