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

Nov 20, 2015

You can use FOIL to find:

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

#### Explanation:

The FOIL mnemonic helps you to enumerate all the possible combinations of one term from the first binomial and one term from the second when multiplying two binomials.

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

$= \stackrel{\text{First" overbrace ((-3*2)) + stackrel "Outside" overbrace ((-3 * 7i)) + stackrel "Inside" overbrace ((i*2)) + stackrel "Last}}{\overbrace{\left(i \cdot 7 i\right)}}$

$= - 6 - 21 i + 2 i + 7 {i}^{2}$

$= - 6 - 21 i + 2 i - 7$

$= - 13 - 19 i$