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Câu hỏi: Cho số phức $z=a+bi$ $\left( a,b\in \mathbb{R} \right)$ thoả mãn $z-2\bar{z}=-1+5i$. Giá trị $a+b$ bằng?
A. $-\dfrac{8}{3}$
B. $\dfrac{8}{3}$.
C. $-\dfrac{2}{3}$.
D. $\dfrac{2}{3}$
A. $-\dfrac{8}{3}$
B. $\dfrac{8}{3}$.
C. $-\dfrac{2}{3}$.
D. $\dfrac{2}{3}$
Ta có: $\left( a+bi \right)-2\left( a-bi \right)=-1+5i$ $\Leftrightarrow a+bi-2a+2bi=-1+5i$
$\Leftrightarrow \left\{ \begin{aligned}
& -a=-1 \\
& 3b=5 \\
\end{aligned} \right. $ $ \Leftrightarrow \left\{ \begin{aligned}
& a=1 \\
& b=\dfrac{5}{3} \\
\end{aligned} \right.$
Vậy $a+b=1+\dfrac{5}{3}=\dfrac{8}{3}$
$\Leftrightarrow \left\{ \begin{aligned}
& -a=-1 \\
& 3b=5 \\
\end{aligned} \right. $ $ \Leftrightarrow \left\{ \begin{aligned}
& a=1 \\
& b=\dfrac{5}{3} \\
\end{aligned} \right.$
Vậy $a+b=1+\dfrac{5}{3}=\dfrac{8}{3}$
Đáp án B.