Question
If ω is the complex cube root of unity, show that
$(a+b)^2+\left(a \omega+b \omega^2\right)^2+\left(a \omega^2+b \omega\right)^2=6 a b$
$(a+b)^2+\left(a \omega+b \omega^2\right)^2+\left(a \omega^2+b \omega\right)^2=6 a b$
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