# How do you simplify (1 + 5i) (1 - 5i) ?

Jan 4, 2016

$\left(1 + 5 i\right) \left(1 - 5 i\right) = 26$

#### Explanation:

$\left(1 + 5 i\right) \left(1 - 5 i\right)$
use the difference of squares formula:$\left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$
so in this case:
$\left(1 + 5 i\right) \left(1 - 5 i\right) = {\left(1\right)}^{2} - {\left(5 i\right)}^{2}$=>simplify:
$= 1 - \left({5}^{2} \cdot {i}^{2}\right)$=>simplify: ${i}^{2} = - 1$:
$= 1 - \left(25 \cdot \left(- 1\right)\right)$
$= 1 - \left(- 25\right)$
$= 1 + 25$
$= 26$

Or you may just use the FOIL method to distribute the parenthesis.
FOIL means First, Outside, Inside, Last:
$\left(1 + 5 i\right) \left(1 - 5 i\right)$
$= 1 - 5 i + 5 i - 25 {i}^{2}$
$= 1 + 25$
$= 26$