Có bao nhiêu số phức z thỏa mãn z^2 + z ngang = 0. Có 2 số

* Hướng dẫn giải

Đáp án C

$$\begin{gathered} Đặt z=a+bi (a;b\in \mathrm{ℝ}) \\ \Rightarrow {\mathrm{z}}^2+\overline{\mathrm{z}}={\mathrm{a}}^2-{\mathrm{b}}^2+2\mathrm{abi}+\mathrm{a}-\mathrm{bi}=0 \\ \iff \left\{\begin{array}{l}{\mathrm{a}}^2-{\mathrm{b}}^2+\mathrm{a}=0\\ 2\mathrm{ab}-\mathrm{b}=0\end{array}\right.\iff \left\{\begin{array}{l}{\mathrm{a}}^2+\mathrm{a}-{\mathrm{b}}^2=0\\ \mathrm{b}(2\mathrm{a}-1)=0\end{array}\right. \\ \mathrm{TH}1: \mathrm{b}=0 \Rightarrow {\mathrm{a}}^2+\mathrm{a}=0\iff \mathrm{a}=\pm 1 \\ \Rightarrow \mathrm{Có} 2 \mathrm{số} \mathrm{phức} \mathrm{z}=0 \mathrm{và} \mathrm{z}=\pm 1 \\ \mathrm{TH}2: \mathrm{a}=\frac{1}{2}\Rightarrow \frac{3}{4}-{\mathrm{b}}^2=0\iff \mathrm{b}=\pm \frac{\sqrt{3}}{2} \\ \Rightarrow \mathrm{Có} 2 \mathrm{số} \mathrm{phức} \mathrm{z}=\frac{1}{2}+\mathrm{i}\frac{\sqrt{3}}{2} \mathrm{và} \mathrm{z}= \frac{1}{2}-\mathrm{i}\frac{\sqrt{3}}{2} \\ \mathrm{KL}: \mathrm{Có} 4 \mathrm{số} \mathrm{phức} \mathrm{thỏa} \mathrm{mãn} \mathrm{bài} \mathrm{toán} \end{gathered}$$