求满足方程

的复数 $z$。答案以 $x+\mathrm{i}y$ 的形式表示，其中 $x$ 和 $y$ 为实数。

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。

先交叉相乘，设实部与虚部后得到两个一次方程。

Let $z=x+y\mathrm{i}$. Cross-multiplying,

Expanding the right-hand side gives

Comparing parts,

Thus

Using $x=9+3y$ in the second equation gives $y=-2$, and then $x=3$. Therefore

This has $z+3\mathrm{i}=3+\mathrm{i}\ne0$, so it is valid.

也可直接把复数 $z$ 当作未知量移项求解，再将结果分母实数化。

Cross-multiplying and expanding,

Hence

so

The original denominator is nonzero for this value.