# How do you simplify (-6-8i)(-3+8i)?

Jun 6, 2017

$82 - 24 i$

#### Explanation:

You can just multiply everything out as in regular brackets, remembering that ${i}^{2} = - 1$.
So the expansion of $\left(- 6 - 8 i\right) \left(- 3 + 8 i\right)$ is:
$\left(- 6\right) \left(- 3\right) + \left(- 6\right) \left(8 i\right) + \left(- 8 i\right) \left(- 3\right) + \left(- 8 i\right) \left(8 i\right)$
$= 18 - 48 i + 24 i - 64 {i}^{2}$
$= 18 - 64 {i}^{2} + \left(- 48 + 24\right) i$
$= 18 + \left(- 64\right) \cdot \left(- 1\right) - 24 i$
$= 18 + 64 - 24 i$
$= 82 - 24 i$

Jun 6, 2017

$82 - 24 i$

#### Explanation:

$\text{expand the brackets using FOIL}$

$\Rightarrow \left(- 6 - 8 i\right) \left(- 3 + 8 i\right)$

$= 18 - 48 i + 24 i - 64 {i}^{2} \leftarrow {i}^{2} = - 1$

$= 18 - 24 i + 64$

$= 82 - 24 i$