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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers2 Marks
MCQ
Real part of $e ^{ i \theta}$ is
  • ✓
    $e ^{\cos \theta}[\cos (\sin \theta)]$
  • B
    $e^{\cos \theta}[\cos (\cos \theta)]$
  • C
    $e ^{\sin \theta}[\sin (\cos \theta)]$
  • D
    $e^{\sin \theta}[\sin (\sin \theta)]$
✓

Answer

Correct option: A.
$e ^{\cos \theta}[\cos (\sin \theta)]$
(A)
$e ^{ i \theta}= e ^{\cos \theta+ i \sin \theta}= e ^{\cos \theta}\left[ e ^{ i \sin \theta}\right]$
$= e ^{\cos \theta}[\cos (\sin \theta)+ i \sin (\sin \theta)]$
∴ Real part of $e ^{ i \theta}$ is $e ^{\cos \theta}[\cos (\sin \theta)]$.

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