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4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
If $\omega = \frac{{ - 1 + \sqrt 3 i}}{2}$then ${(3 + \omega + 3{\omega ^2})^4}$=
  • A
    $16$
  • B
    $-16$
  • ✓
    $16 \omega $
  • D
    $16 {\omega ^2}$
✓

Answer

Correct option: C.
$16 \omega $
c
(c)${(3 + \omega + 3{\omega ^2})^4} = [{(3 + 3{\omega ^2} + \omega )^4}]$
$ = {[\,3\,(1 + {\omega ^2}) + \omega ]^4}$$ = {[3( - \omega ) + \omega ]^4}$
.$= {[\, - 2\omega ]^4} = 16{\omega ^4} = 16\omega $

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