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

If omega is an imaginary cube root of unity, then a root of equation |(x+1,omega,omega^2),(omega,x+omega^2,1),(omega^2,1,x+2)|=0,can be

If omega is a non-real cube root of unity,then the value of (1-omega+omega^(2))^(5)+(1+omega-omega^(2))^(5) is

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

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

If omega is an imaginary cube root of unity, then the value of |(1,omega^(2),1-omega^(4)),(omega,1,1+omega^(5)),(1,omega,omega^(2))| is