Tìm số phức  z  thỏa mãn 

A

- Hướng dẫn giải

Đáp án A.

$$\begin{gathered} \overline{z}=\frac{1}{3}\left[{\left(\overline{1-2i}\right)}^2-z\right]=\frac{1}{3}\left[{\left(1+2i\right)}^2-z\right] \\ =\frac{1}{3}\left(-3;4i-z\right)\iff 3\overline{z}=-3+4i-z \end{gathered}$$

Đặt:

$$\begin{gathered} z=a+bi\Rightarrow 3\left(a-bi\right)=-3+4i-\left(a+bi\right) \\ \iff 3a-3bi=-3-a+\left(4-b\right)i\iff \left\{\begin{array}{l}3a=-3-a\\ 3b=b-4\end{array}\right. \\ \iff \left\{\begin{array}{l}a=-\frac{3}{4}\\ b=-2\end{array}\right.\to z=-\frac{3}{4}-2i. \end{gathered}$$