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If omega ne 1 is a cubic root of unit an...

If `omega ne` 1 is a cubic root of unit and `(1 + omega)^(7)` = A + B`omega`, then (A, B) equals

A

`(-1,1)`

B

`(0,1)`

C

`(1,1)`

D

`(1,0)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(1+ omega)^(7) = A + Bomega `
` therefore (-omega^(2))^(7) = A + Bomega`
`therefore -omega^(2) = A Bomega `
`therefore 1+ omega = A + Bomega `
`therefore A = 1 , B = 1`
` therefore (A,B) = (1,1)`
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