Cho hai số phức

C

- Hướng dẫn giải

Đáp án C.

Ta có $$\begin{gathered} 1=\left(z_1-z_2\right)\overline{\left(z_1-z_2\right)}=\left(z_1-z_2\right)\overline{\left(z_1-z_2\right)}={\left|z_1\right|}^2+{\left|z_2\right|}^2-\left(z_1\overline{z_2}+z_2\overline{z_1}\right)\iff z_1\overline{z_2}+z_2\overline{z_1}=1 \\ P={\left(\frac{z_1}{z_2}\right)}^2+{\left(\frac{z_2}{z_1}\right)}^2={\left(\frac{z_1}{z_2}+\frac{z_2}{z_1}\right)}^2-2={\left(\frac{z_1\overline{z_2}}{{\left|z_2\right|}^2}+\frac{z_2\overline{z_1}}{{\left|z_1\right|}^2}\right)}^2-2={\left(z_1\overline{z_2}+z_2\overline{z_1}\right)}^2-2=-1. \end{gathered}$$.