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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers2 Marks
MCQ
$\left(-\frac{1}{2}+\frac{\sqrt{3}}{2} i\right)^{1000}=$
  • A
    $\frac{1}{2}+\frac{\sqrt{3}}{2} i$
  • B
    $\frac{1}{2}-\frac{\sqrt{3}}{2} i$
  • ✓
    $-\frac{1}{2}+\frac{\sqrt{3}}{2} i$
  • D
    None of these
✓

Answer

Correct option: C.
$-\frac{1}{2}+\frac{\sqrt{3}}{2} i$
(C)
Since $\omega=-\frac{1}{2}+\frac{1}{2} i \sqrt{3}$
$\therefore \quad \omega^{1000}=\omega^{999} \omega=\left(\omega^3\right)^{333} \omega=\omega=-\frac{1}{2}+\frac{\sqrt{3}}{2} i$

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