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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers2 Marks
MCQ
The value of
$\left(1+2 \omega+\omega^2\right)^{3 n}-\left(1+\omega+2 \omega^2\right)^{3 n}=$
  • ✓
    $0$
  • B
    1
  • C
    $\omega$
  • D
    $\omega^2$
✓

Answer

Correct option: A.
$0$
(A)
$\left[\left(1+\omega+\omega^2\right)+\omega\right]^{3 n}-\left[\left(1+\omega+\omega^2\right)+\omega^2\right]^{3 n}$
$=\omega^{3 n}-\left(\omega^2\right)^{3 n}$
$=\left(\omega^3\right)^{ n }-\left(\omega^3\right)^{2 n }$
$=1^n-1^{2 n}$
$=0$

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