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If alpha, beta, gamma in {1,omega,omega^...

If `alpha`, `beta`, `gamma in {1,omega,omega^(2)}` (where `omega` and `omega^(2)` are imaginery cube roots of unity), then number of triplets `(alpha,beta,gamma)` such that `|(a alpha+b beta+c gamma)/(a beta+b gamma+c alpha)|=1` is

A

`3`

B

`6`

C

`9`

D

`12`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` As `|(aalpha+bbeta+cgamma)/(a beta+bgamma+calpha)|=1`
`implies` When `alpha`, `beta`, `gamma` are different, then number of triplet `(alpha,beta,gamma)=` permutation of `1`, `omega` and `omega^(2)=6` and when `alpha-beta=gamma`, number of triplets `=3`.
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