Question

How do you multiply `(1+3i) (5-3i)`?

Answer 1

`5-3i+15i+9=14+12i`

Explanation:

We use FOIL (First, Outside, Inside, Last), like this:

`(1+3i)(5-3i)`

`F: 1 xx 5 = color(white)(000000000000000000000) 5`
`O: 1 xx -3i = color(white)(00000000000000) -3i`
`I: 3i xx 5 = color(white)(0000000000000000000) 15i`
`L: 3i xx -3i = -9i^2=9(-1)=9`

And now we add them all up:

`5-3i+15i+9=14+12i`