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If omega!=1 is a cube root of unity a...

If `omega!=1` is a cube root of unity and `x+y+z!=0,` then prove that `|x/(1+omega)y/(omega+omega^2)z/(omega^2+1)y/(omega+omega^2)z/(omega^2+1)x/(1+omega)(z z)/(omega^2+1)x/(1+omega)y/(omega+omega^2)|=0` if `x=y=z`

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