求方程 $z^3=7\sqrt{3}-7\mathrm{i}$ 的根，将答案写成 $r\mathrm{e}^{\mathrm{i}\theta}$ 的形式，其中 $r\gt0$ 且 $-\pi\le\theta<\pi$。

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。

先求右边的模和辐角。开三次根后，模开立方，三个辐角相差 $\frac{2\pi}{3}$，再移到题给区间。

The modulus is $\sqrt{(7\sqrt3)^2+(-7)^2}=14$. The number lies in the fourth quadrant and $\tan\arg z^3=-1/\sqrt3$, so its argument is $-\pi/6$. Thus $7\sqrt3-7\mathrm{i}=14e^{-\mathrm{i}\pi/6}$. Its cube roots have modulus $14^{1/3}$ and arguments $-\pi/18+2k\pi/3$, where $k$ is an integer. Thus the roots in the required form are