The general value of θ which satisfies the equation ( +i )( 3 +i 3 ) [ (2 n-1) +i (2 n-1)…

Mathematics · JEE Main · NTA ExamsComplex Numbers and Quadratic Equations

The general value of θ which satisfies the equation \((\cos \theta+i \sin \theta)(\cos 3 \theta+i \sin 3 \theta) \ldots[\cos (2 n-1) \theta+i \sin (2 n-1) \theta]=1\)

(where r = 0, 1, 2, 3, ...)

  1. \(\frac{m}{n^{2}}\)
  2. \(\frac{(n-1) \pi}{n^{2}}\)
  3. \(\frac{(2 r+1) n}{n^{3}}\)
  4. \(\frac{2 r \pi}{n^{2}}\)

Answer

(D) 2 r n^ 2

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