# How do you simplify (-3 + i)(2 + 7i) ?

Jan 22, 2016

$\left(- 3 + i\right) \left(2 + 7 i\right) = - 13 - 19 i = - \left(13 + 19 i\right)$

#### Explanation:

Remembering that ${i}^{2} = - 1$

You can think that $\left(a + i b\right)$ is like a binomial, thus:

$\left(- 3 + i\right) \left(2 + 7 i\right) = \left(- 3 \times 2 - 3 \times 7 i + 2 \times i + 7 {i}^{2}\right) =$

$= - 6 - 21 i + 2 i + 7 \times \left(- 1\right) = \left(- 6 - 7\right) + \left(- 21 + 2\right) i = - 13 - 19 i = - \left(13 + 19 i\right)$