Question

How do you simplify `i^6(2i-i^2-3i^3)`?

Answer 1

The answer is -1-5i

Explanation:

First we factorize powers of i.So `i^6` would become -1. `3i^3` would become -3i and `i^2` would become -1.By putting values
`-1(2i-(-1)+3i)`. Now `-1(2i+3i+1)` would become `-1(5i+1)` and then `-5i-1`
I HOPE IT HELPS:)

Answer 2

See details below

Explanation:

Expand expresion.

`i^6(2i-i^2-3i^3)=2i^7-i^8-3i^9`

But we know that:

`i^1=i`
`i^2=-1` (by definition)
`i^3=i^2·i=-i`
`i^4=i^2·i^2=(-1)·(-1)=1`
`i^5=i^4·i=1·i=i` and starts again
`i^6=i^5·i=i·i=i^2=-1`
`i^7=i^6·i=-i`

for this cliclic result, we can write:

`i^6(2i-i^2-3i^3)=2i^7-i^8-3i^9=-2i-1-3i=-1-5i`