# How do you simplify (3-5i)(4+6i)?

Aug 8, 2018

$42 - 2 i$

#### Explanation:

$\left(3 - 5 i\right) \left(4 + 6 i\right)$

First multiply the first values:
$3 \cdot 4 = 12$

Outer values:
$3 \cdot 6 i = 18 i$

Inner values:
$- 5 i \cdot 4 = - 20 i$

Last values:
$- 5 i \cdot 6 i = - 30 {i}^{2}$

Combine them all together:
$12 + 18 i - 20 i - 30 {i}^{2}$

Combine like terms:
$12 - 2 i - 30 {i}^{2}$

We know that ${i}^{2}$ is equivalent to $- 1$, so:
$12 - 2 i - 30 \left(- 1\right)$

Simplify:
$12 - 2 i + 30$

$42 - 2 i$

Hope this helps!