PYQ 2021 : Complex Numbers : If w is cube root of unity, then (3+5w+3w²)² (3+3w+5w²)² is

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PYQ 2022 : Complex Numbers: If α & β are complex cube roots of unity, then α³+β³+α−²β−² is equal to PYQ 2022 : Complex Numbers: If α & β are complex cube roots of unity, then α³+β³+α−²β−² is equal to
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if 1 w and w^2 are cube root of unity , prove that (3+3w+5w^2)^6-(3+w+2w^2)^3=0 if 1 w and w^2 are cube root of unity , prove that (3+3w+5w^2)^6-(3+w+2w^2)^3=0
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