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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers2 Marks
MCQ
If $\omega$ is a complex cube root of unity, then $\left(2+5 \omega+2 \omega^2\right)^6=$
  • A
    18
  • B
    $0$
  • ✓
    729
  • D
    $3 \omega$
✓

Answer

Correct option: C.
729
(C)
$\left(2+5 \omega+2 \omega^2\right)^6=\left[2\left(1+\omega^2\right)+5 \omega\right]^6$
$=[2(-\omega)+5 \omega]^6$
$=[-2 \omega+5 \omega]^6$
$=(3 \omega)^6$
$=3^6 \cdot \omega^6$
$=729$

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