# How do you multiply (1+4i)(3+6i)?

Sep 25, 2016

FOIL

#### Explanation:

Multiply the First terms in each set of parenthesis. $1 \times 3 = 3$
Multiply the Outer terms of each set of parenthesis. $1 \times 6 i = 6 i$
Multiply the Inner terms of each set of parenthesis. $4 i \times 3 = 12 i$
Multiply the Last terms in each set of parenthesis.
$4 i \times 6 i = 24 {i}^{2} = - 24$
First, Outer, Inner, Last - FOIL

So, the answer would be $3 + 6 i + 12 i - 24$
Add like terms: $6 i + 12 i = 18 i$ , $3 - 24 = - 21$

$\left(1 + 4 i\right) \left(3 + 6 i\right) = - 21 + 18 i$