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STD 11 - 4.1 complex nubers — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 4.1 complex nubers4 Marks
MCQ
If $x + \frac{1}{x} = 2\cos \theta ,$ then $x$ is equal to
  • A
    $\cos \theta + i\,\sin \theta $
  • B
    $\cos \theta - i\,\sin \theta $
  • ✓
    $\cos \theta \pm i\,\sin \theta $
  • D
    $\sin \theta \pm i\,\cos \theta $
✓

Answer

Correct option: C.
$\cos \theta \pm i\,\sin \theta $
c
(c) $x + \frac{1}{x} = 2\cos \theta $$ \Rightarrow \,{x^2} - 2x\cos \theta + 1 = 0$
==> $x = \frac{{2\cos \theta \pm \sqrt {4{{\cos }^2}\theta - 4} }}{2}$ ==> $x = \cos \theta \pm i\sin \theta $.

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