Ta có
$z = 4 + 3i- \dfrac{5+2i}{3 - 4i}$
$= 4 + 3i - \dfrac{(5+2i)(3 + 4i)}{9 + 16}$
$= 4 + 3i - \dfrac{7 + 26i}{25}$
$= \dfrac{100 + 75i - 7 - 26i}{25}$
$= \dfrac{93 + 49i}{25}$
$= \dfrac{93}{25} + \dfrac{49}{25}i$
Vậy
$|z|^2 = \dfrac{93^2}{25^2} + \dfrac{49^2}{25^2} = \dfrac{442}{25}$
Vậy $|z| = \dfrac{\sqrt{442}}{5}$.