If `omega` be an imaginary cube root of unity, show that `(1+omega-omega^2)(1-omega+omega^2)=4`

If omega be an imaginary cube root of unity, show that (a+bomega+comega^2)/(aomega+bomega^2+c) = omega^2

If omega is an imainary cube root of unity,then show that (1-omega+omega^(2))^(5)+(1+omega-omega^(2))^(5)=32

If omega is an imainary cube root of unity,then show that (1-omega)(1-omega^(2))(1-omega^(4))(1-omega^(5))=9

If omega be an imaginary cube root of unity, show that: 1/(1+2omega)+ 1/(2+omega) - 1/(1+omega)=0 .

If omega is an imaginary cube root of unity, then (1+omega-omega^(2))^(7) equals

If omega is a cube root of unity, prove that (1+omega-omega^2)^3-(1-omega+omega^2)^3=0

If omega be an imaginary cube root of unity, show that 1+omega^n+omega^(2n)=0 , for n=2,4 .

If omega be imaginary cube root of unity then (1-omega+omega^(2))^(5)+(1+omega-omega^(2))^(5) is equal to (a) 0 (b) 32 (c) 49 (d) none of these