Prove that `(1-omega+omega^2)^3=(1+omega-omega^2)^3=-8`

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

If 1,omega,omega^(2) are the roots of unity then (1-omega+omega^(2))^(3)+(1+omega-omega^(2))^3=

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

If omega is cube roots of unity, prove 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)]=[(0),(0),(0)]

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

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 1,omega,omega^(2) are the cube roots of units then find (1-omega+omega^(2))^(4)+(1+omega-omega^(2))^(8)

If 1, omega, omega^2 be the three cube roots of 1, then show that: (1+omega)(1+omega^2)(1+omega^4)(1+omega^8)=1

Show that (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8))...... to 2 n factors =2^(2n)

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]