在阿根图的草图上，用阴影表示满足不等式 $|z+2-3\mathrm{i}|\leq2$ 和 $\arg z\leq\frac34\pi$ 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。

模条件给出圆心 $(-2,3)$、半径 $2$ 的闭圆盘。整个圆盘在上半平面，辐角条件因此选择射线 $y=-x$ 的顺时针一侧。

Write $z=x+y\mathrm{i}$. The first condition gives

Draw this circle, with centre $(-2,3)$ and radius $2$.

The boundary $\arg z=3\pi/4$ is the ray from the origin through the second quadrant along $y=-x$.

The disc lies entirely above the real axis. Therefore the condition $\arg z\le3\pi/4$ selects points with $y\ge-x$. Shade the intersection of this half-plane and the disc, including both boundaries.