`omega` is an imaginary root of unity. Prove that If `a+b+c=0,` then prove that `(a+bomega+comega^2)^3+(a+bomega^2+comega^)^3=27a b cdot`

omega is an imaginary root of unity. Prove that (i) ( a + bomega + comega^(2))^(3) + (a+bomega^(2) + comega)^(3) = (2a-b-c)(2b -a -c)(2c -a-b) (ii) If a+b+c = 0 then prove that (a + bomega + comega^(2))^(3)+(a+bomega^(2) + comega)^(3) = 27abc .

omega is an imaginary root of unity.Prove that (a+b omega+c omega^(2))^(3)+(a+b omega^(2)+c omega)^(3)=(2a-b-c)(2b-a-c)(2c-a-b)

If omega is an imaginary cube root of unity.Then the equation whose roots are 2 omega+3 omega^(2),2 omega^(2)+3 omega, is

If omega is an imaginary cube root of unity then the equation whose roots are 2 omega+3 omega^(2) and 2 omega^(2)+3 omega is

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

If,omega,omega'2be the imaginary cube roots of unity,then prove that (2-omega)(2-omega^(2))(2-omega^(10))(2-omega^(11))=49

If omega is an imaginary cube root of unity, then the value of |(a,b omega^(2),a omega),(b omega,c,b omega^(2)),(c omega^(2),a omega,c)| , is

If omega is a cube root of unity, prove that (a+bomega+comega^2)/(c+aomega+bomega^2)=omega^2