`(a+omega b+omega^(2)c)(a+omega^(2)b+omega c)=a^(2)+b^(2)+c^(2)-ab-bc-ca`

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

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

If 1 , omega , omega^(2) are the cube roots of unity prove that (a + b) ( a omega + b omega^(2))(aomega^(2) + b omega) = a^(3) + b^(3)

If omega ne 1" and "omega^(3)=1 , the (a omega+b + c omega^(2))/(a omega^(2)+b omega+c)+(a omega^(2)+b+c omega)/(a+b omega+c omega^(2)) is equal to

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 omega is a complex cube root of unity, then (a+b omega+c omega^(2))/(c+a omega+b omega^(2))+(c+a omega+b omega^(2))/(a +b omega+c omega^(2))+(b+c omega+a omega^(2))/(b+c omega+a omega^(5))=

If omega ne 1 and omega^3=1 then (a omega+b+c omega^2)/(a omega^2+b omega+c)+(a omega^2+b+c omega)/(a+b omega+ c omega^2) is equal to a)2 b) omega c) 2 omega d) 2 omega^2