Kí hiệu 

- Hướng dẫn giải

Đáp án cần chọn là: D

$$\begin{gathered} z^2+z+1=0 \\ ∆=1-4=-3=3i^2 \end{gathered}$$

Suy ra $z=\frac{-1\pm i\sqrt{3}}{2}$

Hay $z=-\frac{1}{2}\pm \frac{\sqrt{3}}{2}i$

$$\begin{gathered} \Rightarrow P={\left(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\right)}^2+{\left(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\right)}^2+\left(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\right)\left(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\right) \\ =-\frac{1}{2}-\frac{\sqrt{3}}{2}i-\frac{1}{2}+\frac{\sqrt{3}}{2}i+\frac{1}{4}+\frac{3}{4}=0 \end{gathered}$$