Question

How do you simplify `(8i)(-4i)`?

Answer 1

`32`

Explanation:

When performing the basic mathematical functions on terms that contain `i` within them, it is easiest to recognize it as a variable when starting off.

We can begin to treat this as a normal multiplication problem:

`(8i)(-4i)`

`=-32i^2`

Now that we have this, we need to understand how setting `i` to a power other than `1` changes the value.

`i^0=1`
`i^1=sqrt(-1)`
`i^2=-1`
`i^3=-i`
`i^4=1`
`i^5=sqrt(-1)`
`...`

(Click here for more information regarding imaginary numbers)

In this instance, however, the `i^2` would then become `-1`.

Knowing this we can write our expression as:

`-32(-1)`

`=32`

Answer 2

`32`

Explanation:

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

`rArr(8i)(-4i)`

`=-32i^2=-32xx-1=32`