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

Jul 6, 2016

7 - 2i

#### Explanation:

We require to know the following fact.

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder}}$

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

$\Rightarrow \left(- 3 i\right) \left(3 i\right) = - 9 {i}^{2} = \left(- 9 \times - 1\right) = 9$

hence $\left(- 3 i\right) \left(3 i\right) - \left(2 + 2 i\right) = 9 - 2 - 2 i = 7 - 2 i$