Giả sử: $z=a+bi$

$\left( 1 \right)\Leftrightarrow \left| 2+i \right|\left( a+bi \right)+\frac{2\left( 1+2i \right)}{1+i}=7+8i$

$\Leftrightarrow 2a+2bi+ai+b{{i}^{2}}+\frac{2\left( 1+2i \right)\left( 1-i \right)}{1+{{i}^{2}}}=7+8i$

$\Leftrightarrow 2a+2bi+ai-bi+1-i+2i-2{{i}^{2}}=7+8i\Leftrightarrow \left\{ \begin{align}  & 2a-b+3=7 \\  & 2b+a+1=8 \\ \end{align} \right.$$\Leftrightarrow \left\{ \begin{align}  & a=3 \\  & b=2 \\ \end{align} \right.\Rightarrow z=3+2i$

=> B, C, D đúng