If α, β, γ are the cube roots of a negative number p, then for any three real numbers x…

Mathematics · JEE Advanced · NTA ExamsComplex Numbers and Quadratic Equations

If α, β, γ are the cube roots of a negative number p, then for any three real numbers x, y, z the value of \(\frac{x \alpha+y \beta+z \gamma}{x \beta+y \gamma+z \alpha}\) is
  1. \(\frac{1-i \sqrt{3}}{2}\)
  2. \(\frac{-1-\mathrm{i} \sqrt{3}}{2}\)
  3. (x + y + z) i
  4. π

Answer

(B) -1- i 3 2

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