Let 1, ω, \omega ^{2} be three cube roots of unity. If x = a + b y = a\omega + b\omega ^{2},z = a\omega ^{2} + b\omega then what is x^{2} + y^{2} + z^{2} equal to?

UPSC NDA II 2025 Mathematics Paper

Question : 17 of 120

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Let 1, ω, ω2 be three cube roots of unity. If x = a + b y=aω+bω2,z=aω2+bω then what is x2+y2+z2 equal to?

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