Explanation

(c)
Let $z = \frac{1 - i}{3 + i} + \frac{4i}{5}$
$= \frac{5 - 5i + 12i - 4}{5(3 + i)} = \frac{1 + 7i}{5(3 + i)}$
$= \frac{(1 + 7i)(3 - i)}{5(9 + 1)} = \frac{10 + 20i}{50} = \frac{1 + 2i}{5}$
$\therefore\ \ \ \ \ |z| = \sqrt{\left( \frac{1}{5} \right)^{2} + \left( \frac{2}{5} \right)^{2}} = \frac{1}{5}\sqrt{1 + 4} = \frac{\sqrt{5}}{5}$