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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers2 Marks
MCQ
If $\omega$ is an imaginary cube root of unity, $\left(1+\omega-\omega^2\right)^7$ equals
  • A
    $128 \omega$
  • B
    $-128 \omega$
  • C
    $128 \omega^2$
  • ✓
    $-128 \omega^2$
✓

Answer

Correct option: D.
$-128 \omega^2$
(D)
$\left(1+\omega-\omega^2\right)^7=\left(-\omega^2-\omega^2\right)^7$
$=\left(-2 \omega^2\right)^7$
$=-128 \omega^{14}$
$=-128 \omega^{12} \omega^2$
$=-128 \omega^2$

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