# How do you simplify  (-3 + i)(2 + 7i)  and write in a+bi form?

Dec 22, 2015

Use FOIL then combine terms to find:

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

#### Explanation:

You can use FOIL to multiply the two binomials then combine terms:

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

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

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

$= - 6 - 19 i - 7$

$= - 13 - 19 i$