Question

How do you multiply `(3+2i)(3-2i)`?

Answer 1

`(3+2i)(3-2i)=13`

Explanation:

`(3+2i)(3-2i)`

= `3(3-2i)+2i(3-2i)`

= `3xx3-3xx2i+2ixx3-2ix2i`

= `9-6i+6i-4i^2`

= `9-4(-1)`

= `9+4`

= `13`

Answer 2

13

Explanation:

Distribute the brackets using, for example, the FOIL method.

`(3+2i)(3-2i)=9cancel(-6i)cancel(+6i)-4i^2=9-4i^2`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(i^2=(sqrt(-1))^2=-1)color(white)(a/a)|)))`

`rArr9-4i^2=9+4=13`