(a+b omega+c omega^(2))/(c+a omega+b omega^(2))+(a+b omega+c omega^(2))/(b+c omega+a omega^(2))" is equal to "

Prove the following (a + b omega + c omega^(2))/(c + a omega + b omega^(2)) + (a + b omega + c omega^(2))/(b + c omega + a omega^(2)) = -1

If omega is a complex cube root of unity , then the value of (a + b omega + c omega^(2))/(c + a omega + b omega^(2)) + (a + b omega + comega^(2))/(b + c omega + a omega^(2)) is

If 1 , omega , omega^(2) are the cube roots of unity then the values ((a+b omega+c omega^(2))/(c+a omega+b omega^(2))) + ((a+b omega+c omega^(2))/(b+c omega+a omega^(2))) = (A) 1 (B) 0 (C) -1 (D) None of these

If 1 , omega , omega^(2) are the cube roots of unity , then find the values of the following . [(a + b omega + c omega^(2))/(c + a omega + b omega^(2))] + [(a + b omega +c omega)/( b + c omega + a omega ^(2 ) ] ]

If omega pm 1 is a cube root of unity, show that (a + b omega + c omega^(2))/(b + c omega + a omega^(2))+ (a + b omega + c omega^(2))/(c + a omega + b omega^(2)) = -1

If omega pm 1 is a cube root of unity, the value of (a + b omega + c omega^(2))/(b + c omega + a omega^(2))+ (a + b omega + c omega^(2))/(c + a omega + b omega^(2)) = ?

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 , 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

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