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4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
The value of $\frac{{{i^{592}} + {i^{590}} + {i^{588}} + {i^{586}} + {i^{584}}}}{{{i^{582}} + {i^{580}} + {i^{578}} + {i^{576}} + {i^{574}}}} - 1 = $
  • A
    $ - 1$
  • ✓
    $-2$
  • C
    $ - 3$
  • D
    $-4$
✓

Answer

Correct option: B.
$-2$
b
(b) $\frac{{{i^{584}}({i^8} + {i^6} + {i^4} + {i^2} + 1)}}{{{i^{574}}({i^8} + {i^6} + {i^4} + {i^2} + 1)}} - 1 = \frac{{{i^{584}}}}{{{i^{574}}}} - 1$
$ = {i^{10}} - 1 = - 1 - 1 = - 2$.

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