Cho các số phức z1,z2 với phần ảo tương ứng là b1,b2. Đặt z1'

* Hướng dẫn giải

Đáp án D

$$\begin{gathered} \mathrm{Đặt} {\mathrm{z}}_1=\mathrm{a}+{\mathrm{ib}}_1 \mathrm{và} {\mathrm{z}}_2=\mathrm{c}+{\mathrm{ib}}_2 \\ \Rightarrow \left\{\begin{array}{l}{\mathrm{z}}_1^{\text{'}}=\left(1+\mathrm{i}\right){\mathrm{z}}_1=\left(1+\mathrm{i}\right)\left(\mathrm{a}+{\mathrm{ib}}_1\right)=\mathrm{a}+{\mathrm{ib}}_1+\mathrm{ai}-{\mathrm{b}}_1=\mathrm{a}-{\mathrm{b}}_1+\mathrm{i}(\mathrm{a}+{\mathrm{b}}_1)\\ {\mathrm{z}}_2^{\text{'}}=\left(1+\mathrm{i}\right){\mathrm{z}}_2=\left(1+\mathrm{i}\right)\left(\mathrm{c}+{\mathrm{ib}}_2\right)=\mathrm{c}+{\mathrm{ib}}_2+\mathrm{ci}-{\mathrm{b}}_2=\mathrm{c}-{\mathrm{b}}_2+\mathrm{i}(\mathrm{c}+{\mathrm{b}}_2)\end{array}\right. \\ \Rightarrow \left\{\begin{array}{l}{\mathrm{b}}_1^{\text{'}}=\mathrm{a}+{\mathrm{b}}_1\\ {\mathrm{b}}_2^{\text{'}}=\mathrm{c}+{\mathrm{b}}_2\end{array}\right. \\ \mathrm{Nếu} {\mathrm{b}}_1={\mathrm{b}}_2\Rightarrow {\mathrm{b}}_1^{\text{'}}-{\mathrm{b}}_2^{\text{'}}=\mathrm{a}-\mathrm{c}\iff {\mathrm{b}}_1^{\text{'}}=\left(\mathrm{a}-\mathrm{c}\right)+{\mathrm{b}}_2^{\text{'}} \Rightarrow \mathrm{A} \mathrm{sai} \\ \mathrm{Nếu} {\mathrm{b}}_1^{\text{'}}={\mathrm{b}}_2^{\text{'}} \Rightarrow \mathrm{a}+{\mathrm{b}}_1=\mathrm{c}+{\mathrm{b}}_2 ( \mathrm{a}=\mathrm{c} \mathrm{thì} {\mathrm{b}}_1={\mathrm{b}}_2 )\Rightarrow \mathrm{B} \mathrm{sai} \\ \mathrm{Nếu} {\mathrm{b}}_1=-{\mathrm{b}}_2 \Rightarrow {\mathrm{b}}_1^{\text{'}}+{\mathrm{b}}_2^{\text{'}}=\mathrm{a}+\mathrm{c}+{\mathrm{b}}_1+{\mathrm{b}}_2=\mathrm{a}+\mathrm{c}\Rightarrow \mathrm{C} \mathrm{sai} \\ \overline{{\mathrm{z}}_1}=\overline{{\mathrm{z}}_2}\Rightarrow \left\{\begin{array}{l}\mathrm{a}=\mathrm{c}\\ {\mathrm{b}}_1={\mathrm{b}}_2\end{array}\right. \\ \Rightarrow {\mathrm{b}}_1^{\text{'}}-{\mathrm{b}}_2^{\text{'}}=\mathrm{a}-\mathrm{c}+{\mathrm{b}}_1-{\mathrm{b}}_2=0\iff {\mathrm{b}}_1^{\text{'}}={\mathrm{b}}_2^{\text{'}}\Rightarrow \mathrm{D} \mathrm{đúng} \end{gathered}$$