Let w = cos and α = w + w 2 + w 4 and β = w 3 + w 5 + w 6 . _ k=0 ^ 6 w^ k^ 2 equals :

Mathematics · JEE Advanced · NTA Exams — Complex Numbers and Quadratic Equations

Let w = cos and α = w + w² + w⁴ and
β = w³ + w⁵ + w⁶.
\(\sum_{k=0}^{6} w^{k^{2}}\)equals :

1. i
2. \(\sqrt{7} i\)
3. –i
4. \(-\sqrt{7} i\)

Answer

(B) 7 i

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