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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 $ is an imaginary cube root of unity, ${(1 + \omega - {\omega ^2})^7}$equals
  • A
    $128\omega $
  • B
    $ - 128\omega $
  • C
    $128{\omega ^2}$
  • ✓
    $ - 128{\omega ^2}$
✓

Answer

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

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