Question

If 1, `omega` and `omega^2` are the cube roots of unity, prove `(a + b omega + c omega^2)/(c + s omega +  b omega^2) =  omega^2`

Answer 1

Taking LHS

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

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

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

`= 1/omega xx omega^2/omega^2`

`=  omega^2`