If omega is an imaginary cube root of un...

If `omega` is an imaginary cube root of unity, then `(1+omega-omega^2)^7` is equal to (a) `128omega` (b) `-128omega` (c) `128omega^2` (d) `-128omega^2`

A

`128 omega`

B

`-128 omega`

C

`128 omega^2`

D

`-128 omega^2`

Verified by Experts

The correct Answer is:

D

`(1+omega-omega^2)^7=(-omega^2-omega^2)^7" "[because1+omega+omega^2=0]`
`=(-2 omega^2)^7=(-2)^7omega^(14)=-128 omega^2`

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