# How do you simplify (-1+6i)^2?

Aug 10, 2018

$37 - 12 i$

#### Explanation:

${\left(- 1 + 6 i\right)}^{2}$

$\left(- 1 + 6 i\right) \left(- 1 + 6 i\right)$

Use FOIL to distribute:
$- 1 \cdot - 1 = 1$

$- 1 \cdot 6 i = - 6 i$

$6 i \cdot - 1 = - 6 i$

$6 i \cdot - 6 i = - 36 {i}^{2}$

Combine them all together:
$1 - 6 i - 6 i - 36 {i}^{2}$

Combine like terms:
$1 - 12 i - 36 {i}^{2}$

We know that ${i}^{2}$ = -1, so: 1 - 12i - 36(-1)#

$1 - 12 i + 36$

Simplify:
$37 - 12 i$

Hope this helps!