\(\frac{a+b\omega+c\omega^2}{c+a\omega+b\omega^2}\) = \(\frac{a+b/\omega^2+c\omega^2}{c+a/\omega^2+b\omega^2}\) (\(\because\omega^3=1, \omega=1/\omega^2\))
= \(\frac{a\omega^2+b+c\omega^4}{c\omega^2+a+b\omega^4}\)\(=\frac{b+\omega^2(a+c\omega^2)}{a+\omega(c+b\omega^2)}\)