How do you multiply (2-4i)(3+5i)?

Nov 12, 2016

$\left(2 - 4 i\right) \left(3 + 5 i\right) = 26 - 2 i$

Explanation:

$\left(2 - 4 i\right) \left(3 + 5 i\right) = \left(2\right) \left(3\right) + \left(2\right) \left(5 i\right) + \left(- 4 i\right) \left(3\right) + \left(- 4 i\right) \left(5 i\right)$
$\therefore \left(2 - 4 i\right) \left(3 + 5 i\right) = 6 + 10 i - 12 i - 20 {i}^{2}$
$\therefore \left(2 - 4 i\right) \left(3 + 5 i\right) = 6 - 2 i - 20 {i}^{2}$

Now ${i}^{2} = - 1$, so
$\therefore \left(2 - 4 i\right) \left(3 + 5 i\right) = 6 - 2 i + 20$
$\therefore \left(2 - 4 i\right) \left(3 + 5 i\right) = 6 - 2 i + 20$
$\therefore \left(2 - 4 i\right) \left(3 + 5 i\right) = 26 - 2 i$