复数 $z$ 满足 $|z|=2$ 且 $0\le\arg z\le\frac14\pi$。

(a) 在下方的 Argand 图中，画出表示 $z$ 的点的轨迹草图。

(b) 在同一个图中，画出表示 $z^2$ 的点的轨迹草图。

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。

固定模长给出圆，辐角区间选出第一象限的一段圆弧。这里画弧线，不涂扇形内部。

The locus is the arc of the circle with centre $O$ and radius $2$, from argument $0$ to argument $\pi/4$.

Its endpoints are $(2,0)$ and $(\sqrt2,\sqrt2)$, both included. Draw the arc without shading the sector. The combined diagram is shown in (b).

平方把模长变为原来的平方，辐角加倍。因此较小角范围变成第一象限的整个四分之一圆。

Write $z=2e^{\mathrm{i}\theta}$, where $0\leqslant\theta\leqslant\pi/4$. Then

On the same diagram, draw the first-quadrant quarter-circle arc with centre $O$ and radius $4$, from $(4,0)$ to $(0,4)$, including both endpoints.

Show both arcs clearly and do not shade their interiors.