Question

How do you perform the operation and write the result in standard form given `(2-3i)^2`?

Answer 1

`-5-12i`

Explanation:

`color(orange)"Reminder "color(white)(x)i^2=(sqrt(-1))^2=-1`

`"note that "(2-3i)^2=(2-3i)(2-3i)`

`"expand factors using FOIL"`

`=4-12i+9i^2=-5-12ilarrcolor(red)"in standard form"`

Answer 2

`-5-12i`

Explanation:

First, multiply using the distributive property:

`(2-3i)^{2} = (2-3i)(2-3i)`

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

Then simplify;

`4 - 6i - 6i + 9i^{2} = 4 - 12i + 9(-1)`

`4 - 12i + 9(-1) = 4 - 12i -9`

`4 - 12i - 9 = -5-12i`