Đáp án A

Chọn A
Ta có \(\left( {2 + 3i} \right)z + 4 - 3i = 13 + 4i\)
\( \Leftrightarrow \left( {2 + 3i} \right)z = 9 + 7i\) \( \Leftrightarrow z = \dfrac{{9 + 7i}}{{2 + 3i}}\) \( \Leftrightarrow z = \dfrac{{\left( {9 + 7i} \right)\left( {2 - 3i} \right)}}{{\left( {2 + 3i} \right)\left( {2 - 3i} \right)}}\) \( \Leftrightarrow z = \dfrac{{18 - 27i + 14i - 21{i^2}}}{{{2^2} - {{\left( {3i} \right)}^2}}}\)
\( \Leftrightarrow z = \dfrac{{39 - 13i}}{{13}}\) \( \Leftrightarrow z = \dfrac{{39}}{{13}} - \dfrac{{13}}{{13}}i\) \( \Leftrightarrow z = 3 - i\).
Khi đó \(\left| z \right| = \sqrt {{3^2} + {{\left( { - 1} \right)}^2}} = \sqrt {10} \).