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 $|z+2\mathrm{i}|\le3$ 和 $|z+2\mathrm{i}|\le|z-2+4\mathrm{i}|$ 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。

第一个条件选圆盘，第二个条件比较到两个定点的距离，选垂直平分线靠近圆心的一侧。两个边界都包括在内。

Write $z=x+y\mathrm{i}$. The first inequality is

so draw the closed disk with centre $(0,-2)$ and radius $3$.

The second inequality means that the point is at least as close to $A=(0,-2)$ as to $B=(2,-4)$. Their midpoint is $(1,-3)$, and the perpendicular bisector of $AB$ is $y=x-4$.

Algebraically,

Shade the part of the disk on or above $y=x-4$, including both boundaries. Mark the centre, radius, the points $A,B$, and the midpoint or the corresponding scale clearly.