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Let omega be a complex number such that ...

Let `omega` be a complex number such that `2omega+1=z` where `z=sqrt(-3.)` `If|1 1 1 1-omega^2-1omega^2 1omega^2omega^7|=3k ,` then`k` is equal to : `-1` (2) `1` (3) `-z` (4) `z`

A

1

B

`z`

C

`-z`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
B
Here, `omega` is complex cube root of untiy.
Applying `R_(1) to R_(1) + R_(2) + R_(3)`, then given matrix reduces to
`|{:(,3,0,0),(,1,-omega^(2)-1,omega^(2)),(,1, omega^(2), omega):}| = 3(-1 - omega-omega)=-3z`
`rArr k = -z`
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