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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`
Solution
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`
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