在 Argand 图上，用阴影标出表示满足不等式 $|z-2+\mathrm{i}|\le3$ 且 $|z|\ge|z-2+2\mathrm{i}|$ 的复数 $z$ 的区域。

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。

第一个不等式是圆内区域。第二个比较到 $0$ 与 $2-2\mathrm{i}$ 的距离，分界线是两点连线的垂直平分线。

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

with centre $(2,-1)$ and radius $3$. The second inequality compares distances to $(0,0)$ and $(2,-2)$. Its boundary is the perpendicular bisector through $(1,-1)$, with equation $y=x-2$. Squaring the distances gives

Draw the circle and the line through $(0,-2)$ and $(2,0)$ using solid boundaries. Shade the part of the closed disc on or below the line.