在 Argand 图中，用阴影标出满足不等式 $|z-1+2\mathrm{i}|\le|z|$ 和 $|z-2|\le1$ 的复数 $z$ 所对应的点组成的区域。

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。

距离不等式给出原点与 $(1,-2)$ 连线的垂直平分线一侧；第二个条件是圆心 $(2,0)$、半径 $1$ 的闭圆盘。涂出两者交集。

Write $z=x+y\mathrm{i}$. The condition $|z-1+2\mathrm{i}|\le|z|$ becomes

Expanding,

Its boundary is the perpendicular bisector of the segment joining $O=(0,0)$ and $P=(1,-2)$, whose midpoint is $(1/2,-1)$.

The second condition is the closed disc

with centre $(2,0)$ and radius $1$.

Draw the circle and the line $y=x/2-5/4$, mark $P$, and shade the part of the disc on or below the line, including the boundaries.