Chọn mệnh đề sai trong các mệnh đề dưới đây: z = w ngang

* Hướng dẫn giải

Đáp án C

$$\begin{gathered} \mathrm{Đặt} \mathrm{z}=\mathrm{a}+\mathrm{bi} \mathrm{và} \mathrm{w}=\mathrm{c}+\mathrm{di} (\mathrm{a};\mathrm{b};\mathrm{c};\mathrm{d}\in \mathrm{ℝ}) \\ \mathrm{Xét} \mathrm{đáp} \mathrm{án} \mathrm{A}: \\ \mathrm{z}=\overline{\mathrm{w}}\iff \left\{\begin{array}{l}\mathrm{a}=\mathrm{c}\\ \mathrm{b}=-\mathrm{d}\end{array}\iff \left\{\begin{array}{l}\mathrm{a}=\mathrm{c}\\ -\mathrm{b}=\mathrm{d}\end{array}\iff \overline{\mathrm{z}}=\mathrm{w} ( \mathrm{đúng} )\right.\right. \\ \mathrm{Xét} \mathrm{đáp} \mathrm{án} \mathrm{B} \mathrm{và} \mathrm{D} \\ \mathrm{z}=\overline{\mathrm{w}}\iff \left\{\begin{array}{l}\mathrm{a}=\mathrm{c}\\ \mathrm{b}=-\mathrm{d}\end{array}\right. \\ \Rightarrow {\mathrm{a}}^2+{\mathrm{b}}^2={\mathrm{c}}^2+{\mathrm{d}}^2\iff \sqrt{{\mathrm{a}}^2+{\mathrm{b}}^2}=\sqrt{{\mathrm{c}}^2+{\mathrm{d}}^2} \mathrm{hay} \left|\mathrm{z}\right|=\left|\overline{\mathrm{w}}\right| ( \mathrm{B} \mathrm{đúng}) \\ \mathrm{Mặt} \mathrm{khác}: {\mathrm{z}}^2=\overline{{\mathrm{w}}^2}\iff {(\mathrm{a}+\mathrm{bi})}^2=\overline{{(\mathrm{c}+\mathrm{di})}^2} \\ \iff {\mathrm{a}}^2-{\mathrm{b}}^2+2\mathrm{abi}={\mathrm{c}}^2-{\mathrm{d}}^2-2\mathrm{cdi} \\ \Rightarrow {\mathrm{c}}^2-{\mathrm{d}}^2-2\mathrm{cdi}={\mathrm{c}}^2-{\mathrm{d}}^2-2\mathrm{cdi} ( \mathrm{D} \mathrm{đúng}) \\ \Rightarrow \mathrm{C} \mathrm{sai} \end{gathered}$$