`(2+omega+omega^2)^3+(1+omega-omega^2)^3=(1-3omega+omega^2)^4=1`

(1-omega+omega^(2))(1+omega-omega^(2))=4

Prove that (1-omega-omega^(2))(1-omega+omega^(2))(1+omega-omega^(2))=8

If omega is a non-real cube root of unity, then (1+2omega+3omega^2)/(2+3omega+omega^2)+(2+3omega+omega^2)/(3+omega+2omega^2) is equal to

If omega be a complex cube root of unity,then the number (1-omega-omega^(2))^(3)+(omega-1-omega^(2))^(3)+(omega^(2)-omega-1)^(3) is: a.Divisible by 3 but not by 8 b.Divisible by 8 but not by 3 c.Divisible by both 3 & 8 d.none of these

If omega is a complex cube root of unity,show that ([1 omega omega^(2)omega omega^(2)1 omega^(2)1 omega]+[omega omega^(2)1 omega^(2)1 omega omega omega^(2)1])[1 omega omega^(2)]=[000]

If 1,omega,omega^(2) are cube roots of unity then (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8)) is equal to

(1-omega+omega^(2))^(2)+(1+omega-omega^(2))^(2)=-4

If omega(ne1) is a cube root of unity, then (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8)) …upto 2n is factors, is