# How do you multiply (3+2i)(1-3i)?

Feb 3, 2015

Just as any other polynomial, except whenever you get ${i}^{2}$ you change it to $- 1$

Let's go:

$\left(3 + 2 i\right) \left(1 - 3 i\right) = 3 \cdot 1 + 3 \cdot \left(- 3 i\right) + 2 i \cdot 1 - 2 i \cdot 3 i$
$= 3 - 9 i + 2 i - 6 {i}^{2} = 3 - 7 i + 2 {i}^{2}$

The ${i}^{2}$ changes into $- 1$ so the answer is:

$3 - 7 i + 2 \cdot \left(- 1\right) = 3 + 7 i - 2 = 1 + 7 i$