# How do you simplify (-12-3i)(-12+9i)?

Sep 25, 2016

$171 - 36 i$

#### Explanation:

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

$\left(- 12 - 3 i\right) \left(- 12 + 9 i\right) = 144 - 72 i + 36 i - 27 {i}^{2}$

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

$\Rightarrow 144 - 36 i - 27 {i}^{2} = 144 - 36 i + 27$

$\Rightarrow \left(- 12 - 3 i\right) \left(- 12 + 9 i\right) = 171 - 36 i$