Cho số phức z thỏa mãn (left( {3 + 2i} right)z + {left( {2 – i} right)^2} = 4 + i).

(begin{array}{l}
left( {3 + 2i} right)z + {left( {2 – i} right)^2} = 4 + i Leftrightarrow left( {3 + 2i} right)z = 1 + 5i\
 Rightarrow z = frac{{1 + 5i}}{{3 + 2i}} = frac{{left( {1 + 5i} right)left( {3 – 2i} right)}}{{9 + 4}} = frac{{3 – 2i + 15i + 10}}{{13}} = 1 + i\
{rm{w}} = left( {z + 1} right)overline z  = left( {2 + i} right)left( {1 – i} right) = 2 – 2i + i + 1 = 3 – i\
left| {rm{w}} right| = sqrt {{3^2} + {1^2}}  = sqrt {10} 
end{array})