Question

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

Answer 1

`(1+5i)(1-5i)=26`

Explanation:

`(1+5i)(1-5i)`
use the difference of squares formula:`(a-b)(a+b)=a^2-b^2`
so in this case:
`(1+5i)(1-5i)=(1)^2-(5i)^2`=>simplify:
`=1-(5^2*i^2)`=>simplify: `i^2=-1`:
`=1-(25*(-1))`
`=1-(-25)`
`=1+25`
`=26`

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