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4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
${\left( {\frac{{ - 1 + i\sqrt 3 }}{2}} \right)^{20}} + {\left( {\frac{{ - 1 - i\sqrt 3 }}{2}} \right)^{20}} = $
  • A
    $20\sqrt 3 i$
  • B
    $1$
  • C
    $\frac{1}{{{2^{19}}}}$
  • ✓
    $ - 1$
✓

Answer

Correct option: D.
$ - 1$
d
(d)As $\frac{{ - 1 + i\sqrt 3 }}{2} = \omega $ and $\frac{{ - 1 - i\sqrt 3 }}{2} = {\omega ^2}$
$\therefore \,\,\,{(\omega )^{20}} + {({\omega ^2})^{20}} = {\omega ^{18}}.{\omega ^2} + {\omega ^{39}}.\omega = {\omega ^2} + \omega = - 1$

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