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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 $(2-\omega)\left(2-\omega^2\right)\left(2-\omega^{10}\right)\left(2-\omega^{11}\right)$ is
  • A
    $-47$
  • B
    47
  • ✓
    49
  • D
    $-49$
✓

Answer

Correct option: C.
49
(C)
$(2-\omega)\left(2-\omega^2\right)(2-\omega)\left(2-\omega^2\right)$
$=(2-\omega)^2\left(2-\omega^2\right)^2$
$=\left[(2-\omega)\left(2-\omega^2\right)\right]^2$
$=\left[4-2\left(\omega+\omega^2\right)+\omega^3\right]^2$
$=[4+2+1]^2$
$=49$

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