Let _n= ( 2 n )+i ( 2 n ), i^2=-1, then (x+y _3+z _3^2 ) (x+y _3^2+z _3 ) is equal to

JEE Main Mathematics question

Let , , then is equal to

Answer: (C)

is a primitive cube root of unity, with and . Expanding, the squares give (using

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Question ID VK-013600