# How do you simplify (-10+11i)(4+2i)-(4i)(-8i)(1-8i)?

Nov 8, 2016

$- 94 + 280 i$

#### Explanation:

Simplify $\left(- 10 + 11 i\right) \left(4 + 2 i\right) - \left(4 i\right) \left(- 8 i\right) \left(1 - 8 i\right)$

Let's start by multiplying $\left(- 10 + 11 i\right) \left(4 + 2 i\right)$

Multiply each term in the first binomial by each term in the second.

$- 40 - 20 i + 44 i + 22 {i}^{2} - \left(4 i\right) \left(- 8 i\right) \left(1 - 8 i\right)$

Combine like terms and recall that ${i}^{2} = - 1$

$- 40 + 24 i + 22 \left(- 1\right) - \left(4 i\right) \left(- 8 i\right) \left(1 - 8 i\right)$

$- 40 + 24 i - 22 - \left(4 i\right) \left(- 8 i\right) \left(1 - 8 i\right)$

$- 62 + 24 i - \left(4 i\right) \left(- 8 i\right) \left(1 - 8 i\right)$

Now let's multiply $\left(4 i\right) \left(- 8 i\right)$

$- 62 + 24 i - \left(- 32 {i}^{2}\right) \left(1 - 8 i\right)$

$- 62 + 24 i + 32 {i}^{2} \left(1 - 8 i\right)$

Again, recall that ${i}^{2} = - 1$

$- 62 + 24 i + 32 \left(- 1\right) \left(1 - 8 i\right)$

$- 62 + 24 i - 32 \left(1 - 8 i\right)$

Distribute the $- 32$

$- 62 + 24 i - 32 + 256 i$

Combine like terms

$- 94 + 280 i$