Question

How do you multiply `(4- 5i ) ( 7+ 8i )`?

Answer 1

`68-3i`

Explanation:

We use FOIL:

• `color(red)(F)` - First terms - `(color(red)(a)+b)(color(red)(c)+d)`

`4xx7=28`

• `color(brown)(O)` - Outside terms - `(color(brown)(a)+b)(c+color(brown)d)`

`4xx8i=32i`

• `color(blue)(I)` - Inside terms - `(a+color(blue)b)(color(blue)(c)+d)`

`-5ixx7=-35i`

• `color(green)(L)` - Last terms - `(a+color(green)b)(c+color(green)d)`

`-5ixx8i=-40i^2=-40xx-1=40`

And now add them up:

`28+32i-35i+40=68-3i`