`(1+omega-omega^(2))^(2)`

If omega is a complex cube root of unity, then (1-omega+omega^(2))^(6)+(1-omega^(2)+omega)^(6)=

The value of (1+omega^(2)+2 omega)^(3n)-(1+omega+2 omega^(2))^(3n) is

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

What is the value of |(1,omega,2 omega^(2)),(2,2omega^(2),4 omega^(3)),(3,3 omega^(3),6 omega^(4))| , where omega is the cube root of the unity ?

What is the value of |{:(1,omega,2omega^(2)),(2,2omega^(2),4omega^(3)),(3,3omega^(3),6omega^(4)):}| , where omega is the cube root of unity ?

If omega is a cube root of unity,then find the value of the following: (1+omega-omega^(2))(1-omega+omega^(2))

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