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

Sep 19, 2016

$\left(3 + 2 i\right) \left(3 - 2 i\right) = 13$

#### Explanation:

$\left(3 + 2 i\right) \left(3 - 2 i\right)$

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

= $3 \times 3 - 3 \times 2 i + 2 i \times 3 - 2 i x 2 i$

= $9 - 6 i + 6 i - 4 {i}^{2}$

= $9 - 4 \left(- 1\right)$

= $9 + 4$

= $13$

Sep 19, 2016

13

#### Explanation:

Distribute the brackets using, for example, the FOIL method.

$\left(3 + 2 i\right) \left(3 - 2 i\right) = 9 \cancel{- 6 i} \cancel{+ 6 i} - 4 {i}^{2} = 9 - 4 {i}^{2}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{i}^{2} = {\left(\sqrt{- 1}\right)}^{2} = - 1} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\Rightarrow 9 - 4 {i}^{2} = 9 + 4 = 13$