Cho số phức $z$ thỏa mãn $3\left( \overline{z}+i \right)-\left(...

Gọi $z=a+bi$ $\left( a, b\in \mathbb{R} \right)$
$3\left( \overline{z}+i \right)-\left( 2-i \right)z=3+10i\Leftrightarrow 3\left[ a+\left( 1-b \right)i \right]-\left( 2-i \right)\left( a+bi \right)=3+10i$
$\Leftrightarrow 3a-2a-b+\left( 3-3b+a-2b \right)i=3+10i$
$\Leftrightarrow \left\{ \begin{aligned}
& 3a-2a-b=3 \\
& 3-3b+a-2b=10 \\
\end{aligned} \right.$
$\Leftrightarrow \left\{ \begin{aligned}
& a-b=3 \\
& a-5b=7 \\
\end{aligned} \right.$
$\Leftrightarrow \left\{ \begin{aligned}
& a=2 \\
& b=-1 \\
\end{aligned} \right.$
$\Rightarrow z=2-i\Rightarrow \left| z \right|=\sqrt{5}$,