`(a+b omega+c omega^(2))(a+b omega^(2)+c omega)`

Let omega be a complex cube root of unity with 0

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 a+b+c=0 and omega,omega^(2) are imaginary cube roots of unity,then (a+b omega+c omega^(2))^(2)+(a+b omega^(2)+c omega)^(3)=3abc (b) 6abc (c) 9 abc (d) 27 abc

If a,b,c are distinct integers and a cube root of unity then minimum value of x=|a+b omega+c omega^(2)|+|a+b omega^(2)+c omega|

If a^(3)+b^(3)+6abc=8c^(3)& omega is a cube root of unity then: a,b,c are in Adot P*( b) a,b,c, are in Hdot P*a+b omega-2c omega^(2)=0a+b omega^(2)-2c omega=0

Let omega=e^((i pi)/(3)) and a,b,c,x,y,z be non-zero complex numbers such that a+b+c=x,a+b omega+c omega^(2)=y,a+b omega^(2)+c omega=z Then,the value of (|x|^(2)+|y|^(2)|+|y|^(2))/(|a|^(2)+|b|^(2)+|c|^(2))

(a+b)^(2)+(a omega+b omega^(2))^(2)+(a omega^(2)+b omega)^(2)=

Prove that a^3 + b^3 + c^3 – 3abc = (a + b + c) (a + bomega + comega^2) (a + bomega^2 + "c"omega) , where omega is an imaginary cube root of unity.