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If omega is a non-real cube root of u...

If `omega` is a non-real cube root of unity and `n` is not a multiple of 3, then `=|1omega^nomega^(2n)omega^(2n)1omega^nomega^nomega^(2n)1|` is equal to (a) 0 (b) `omega` (c) `omega^2` (d) 1

Text Solution

Verified by Experts

The correct Answer is:
0
`Delta=1[(omega^(3n)-1)+omega^(n)(omega^(2n)-omega^(2n))+omega^(2n)(omega^(n)-omega^(4n))`
`Delta=[(omega^(3))^(n)-1]+0+omega^(2n)[omega^(n)-(omega^(3))^(n).omega^(n)]," "Delta=1-1+0+omega^(2n)[omega^(n)-omega^(n)]=0`
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