Question

How do you multiply `(4-2i)^2`?

Answer 1

`(4-2i)^2=12-16i`

Explanation:

`(4-2i)^2`

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

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

= `16-8i-8i+4i^2` and as `i^2=-1`

= `16-16i-4`

= `12-16i`

Answer 2

`12-16i`

Explanation:

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

`rArr(4-2i)^2=(4-2i)(4-2i)=16-8i-8i+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)|)))`

`16-8i-8i+4i^2=16-16i-4`

`rArr(4-2i)^2=12-16i`