Argand 图中的阴影区域表示由两个不等式定义的复数 $z$ 所对应的点。阴影区域以一个圆和一条平行于虚轴的直线为边界。阴影区域包含其边界。

(a) 求两个用 $z$ 表示的不等式，以定义这个阴影区域。

(b) 计算这个区域内各点所对应的 $\arg z$ 的最小值。

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。

从图上读出圆心、半径和竖直边界，并根据阴影确定不等号方向。边界包括在内，必须使用非严格不等号。

The circle has centre $1-2\mathrm{i}$ and radius $2$. The shaded part lies inside the circle and to the right of $\operatorname{Re}z=2$.

Including the boundaries, the two inequalities are

最低辐角来自竖直边界与圆的下交点。求交点后，用实部与虚部确定第四象限的负角。

Write $z=x+y\mathrm{i}$. On the lower circular boundary,

As $x$ increases, $y$ increases while remaining negative. Therefore $y/x$ increases, so the least argument occurs at the lower endpoint with $x=2$.

At this point,

Since the point is in the fourth quadrant,

Thus the least argument is $\boxed{-1.08\text{ radians}}$.