Cho phương trình ${{z}^{2}}+2z+5=0 \left( z\in \mathbb{C} \right)$...

Ta có $\Leftrightarrow \left[ \begin{aligned}
& {{z}_{1}}+1=2i \\
& {{z}_{2}}+1=-2i \\
\end{aligned} \right.$$\Leftrightarrow \left[ \begin{aligned}
& {{z}_{1}}=-1+2i \\
& {{z}_{2}}=-1-2i \\
\end{aligned} \right.\left| {{z}_{1}} \right|+\left| {{z}_{2}} \right|=\sqrt{{{\left( -1 \right)}^{2}}+{{2}^{2}}}+\sqrt{{{\left( -1 \right)}^{2}}+{{\left( -2 \right)}^{2}}}=2\sqrt{5}$.