If z^2 + z + 1 = 0 then (z^3 + 1 z^3 )^2 + (z^4 + 1 z^4 )^2 = where z = w = complex cube root of unity

MHT CET 2024 Mathematics question

If then where complex cube root of unity

Answer: (C)

Since , is a non-real cube root of unity () with and . Then , whose square is . Next and (as

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Question ID VK-093003