Question

How do you multiply `(4+5i)(4-5i)`?

Answer 1

We know that

`(a+b)(a-b) = a^2 - b^2`
and that

`i^2 = -1`

It follows

`(4 + 5i)(4 - 5i)`

`= 4^2 - (5i)^2`

`= 16 - (25i^2)`

`= 16 + 25`

`= 41`