Explanation

(b)
Let $z = \frac{\left( 1 - i\sqrt{3} \right)(2 + 2i)}{(\sqrt{3} - i)}$
$= \frac{\left( 2 - 2\sqrt{3} \right) + 2i(1 + \sqrt{3})}{(\sqrt{3} - i)} \times \frac{(\sqrt{3} - i)}{(\sqrt{3} - i)}$
$= \frac{2\sqrt{3} - 6 + 2i - 2\sqrt{3}i + 2\sqrt{3}i + 6i - 2 - 2\sqrt{3}\ }{3 + 1}$
$= \frac{- 8 + 8i}{4} = - 2 + 2i$
$\therefore$ Magnitude of $z = \sqrt{4 + 4} = 2\sqrt{2}$
And amplitude of $z = \tan^{- 1}{\left( \frac{2}{- 2} \right) = \frac{3\pi}{4}}$