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