Let `omega ne 1` be a complex cube root of unity. If `(3-3omega+2omega^(2))^(4n+3) + (2+3omega-3omega^(2))^(4n+3)+(-3+2omega+3omega^(2))^(4n+3)=0`, then the set of possible value(s) of n is are

Options

A. N
B. `{3k: k in N}`
C. `N-(3k:k in N)`
D. `{6k:k in N}`

Answer

C

Explanation

We have,
`(3-3omega+2omega^(2))+(2+3omega-3omega^(2))^(4n+3) +(-3+2omega+3omega^(2))^(4n+3)=0`
`rArr (3-3omega+2omega^(2))^(4n+3)(1+omega^(4n+3))(1+omega^(n)+omega^(2n))=0`
`rArr 1+omega^(n)+omega^(2n)=0`
`rArr` n is not a multiple of 3
Hence, the set of values of n is `N-(n:n=3k, k in N)`