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Câu hỏi: Cho hai số phức ${{z}_{1}}=1-2i, {{z}_{2}}=x-4+yi$ với $\left( x,y\in \mathbb{R} \right)$. Tìm cặp $\left( x;y \right)$ để ${{z}_{2}}=2{{\bar{z}}_{1}}$.
A. $\left( x;y \right)=\left( 4;6 \right)$.
B. $\left( x;y \right)=\left( 5;-4 \right)$.
C. $\left( x;y \right)=\left( 6;-4 \right)$.
D. $\left( x;y \right)=\left( 6;4 \right)$.
A. $\left( x;y \right)=\left( 4;6 \right)$.
B. $\left( x;y \right)=\left( 5;-4 \right)$.
C. $\left( x;y \right)=\left( 6;-4 \right)$.
D. $\left( x;y \right)=\left( 6;4 \right)$.
${{z}_{1}}=1-2i\Rightarrow \overline{{{z}_{1}}}=1+2i\Rightarrow 2\overline{{{z}_{1}}}=2+4i.$
Do đó ${{z}_{2}}=2\overline{{{z}_{1}}}\Leftrightarrow \left\{ \begin{aligned}
& x-4=2 \\
& y=4 \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& x=6 \\
& y=4 \\
\end{aligned} \right..$
Do đó ${{z}_{2}}=2\overline{{{z}_{1}}}\Leftrightarrow \left\{ \begin{aligned}
& x-4=2 \\
& y=4 \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& x=6 \\
& y=4 \\
\end{aligned} \right..$
Đáp án D.