Question

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`

Answer 1

Correct Answer - 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`