Proposition

Find the absolute values of

1. $-2i(3 + i)(2 + 4i)(1 + i)$
2. $\displaystyle\frac{(3 + 4i)(-1 + 2i)}{(-1 - i)(3 - i)}$.

Solution

1. $\abs{-2i(3 + i)(2 + 4i)(1 + i)} = 2 \cdot \sqrt{10} \cdot \sqrt{20} \cdot \sqrt{2} = 40$.
2. $\frac{5 \cdot \sqrt{1 + 4}}{\sqrt{2} \cdot \sqrt{9 + 1}} = 5/2$.