If w is a complex cube root of unity.
`|(a,b,c),(b,c,a),(c,a,b)| = -(a +b +c) (a + bk + ck^(2)) (a + bk^(2) + ck)`, then k equals

If omega is a cube root of unity then |(a,b,c),(b,c,a),(c,a,b)| has a factor

If omega is an imaginary cube root of unity , prove that, |{:(a,b,c),(b,c,a),(c,a,b):}|=-(a+b+c)(a+bomega+comega^2)(a+bomega^2+comega)

If omega is a complex cube root of unity, show that (a+b) + (a omega +b omega^2 )+(a omega^2 +b omega ) =0

If omega is a complex cube root of unity , then the value of (a + b omega + c omega^(2))/(c + a omega + b omega^(2)) + (a + b omega + comega^(2))/(b + c omega + a omega^(2)) is

If omega is a complex cube root of unity, show that (a+b)^2 + (a omega+b omega^2)^2 +(a omega^2 +b omega)^2 =6ab

If omega is a complex cube root of unity, then (a+b omega+c omega^(2))/(c+a omega+b omega^(2))+(c+a omega+b omega^(2))/(a +b omega+c omega^(2))+(b+c omega+a omega^(2))/(b+c omega+a omega^(5))=

If omega (ne 1) is a cube root of unity and (1 + omega^(2))^(11) = a + b omega + c omega^(2) , then (a, b, c) equals

If omega is a complex cube root of unity, show that frac{a+b omega+c omega^2}{c+a omega+b omega^2} = omega^2

If 1, omega and omega^(2) are the cube roots of unity, then (a+b+c) (a+b omega+c omega^(2))(a+b omega^(2) +c omega)=