Mô đun của số phức z thỏa mãn (dfrac{{2 + i}}{{1 – i}}z = dfrac{{ – 1 + 3i}}{{2 + i}}) là:

(begin{array}{l}dfrac{{2 + i}}{{1 – i}}z = dfrac{{ – 1 + 3i}}{{2 + i}}\ Leftrightarrow z = dfrac{{left( { – 1 + 3i} right)left( {1 – i} right)}}{{{{(2 + i)}^2}}}\ Leftrightarrow z = dfrac{{2 + 4i}}{{3 + 4i}}\ Leftrightarrow z = dfrac{{left( {2 + 4i} right)left( {3 – 4i} right)}}{{9 – 16{i^2}}}\ Leftrightarrow z = dfrac{{6 – 16{i^2} + 4i}}{{25}}\ Leftrightarrow z = dfrac{{22}}{{25}} + dfrac{4}{{25}}i\ Rightarrow left| z right| = dfrac{{2sqrt 5 }}{5}end{array})