V(a) If `w` is cube roots of unity then prove that `a^3 +b^3 = (a+b) (aw^4+bw^8) ( aw^2 +bw^7)`

If omega is a cube root of unity, then omega^(3) = ……

If omega is a cube root of unity, then omega + omega^(2)= …..

If omega is a cube root of unity, then 1+ omega^(2)= …..

If 1, omega, omega^(2) are cube roots of unity, prove that (x + y)^(2) + (x omega + y omega^(2))^(2) + (x omega^(2) + y omega)^(2)= 6xy

If 1, omega, omega^(2) are three cube roots of unity, prove that omega^(28) + omega^(29) + 1= 0

If 1, omega, omega^(2) are the cube roots of unity, prove that (1 + omega)^(3)-(1 + omega^(2))^(3)=0

If 1, omega, omega^(2) are three cube roots of unity, prove that (1 + omega - omega^(2)) (1- omega + omega^(2))=4

If 1, omega, omega^(2) are three cube roots of unity, prove that (3+ 5omega + 3omega^(2))^(6) = (3 + 5omega^(2) + 3omega)^(6)= 64

If omega is a non-real cube root of unity, then Delta = |(a_(1) + b_(1) omega,a_(1) omega^(2) + b_(1),a_(1) + b_(1) + c_(1) omega^(2)),(a_(2) + b_(2) omega,a_(2) omega^(2) + b_(2),a_(2) + b_(2) + c_(2) omega^(2)),(a_(3) + b_(3) omega,a_(3) omega^(2) + b_(3),a_(3) + b_(3) + c_(3) omega^(2))| is equal to

If 1, omega, omega^(2) are three cube roots of unity, prove that (1+ omega- omega^(2))^(3)= (1- omega + omega^(2))^(3)= -8