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4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
$\frac{{1 - i}}{{1 + i}}$is equal to
  • A
    $\cos \frac{\pi }{2} + i\sin \frac{\pi }{2}$
  • ✓
    $\cos \frac{\pi }{2} - i\sin \frac{\pi }{2}$
  • C
    $\sin \frac{\pi }{2} + i\cos \frac{\pi }{2}$
  • D
    None of these
✓

Answer

Correct option: B.
$\cos \frac{\pi }{2} - i\sin \frac{\pi }{2}$
b
(b) $\frac{{1 - i}}{{1 + i}} = \frac{{(1 - i)(1 - i)}}{{(1 + i)(1 - i)}} = \frac{{1 + {{(i)}^2} - 2i}}{{1 + 1}} = - i$
which can be written as $\cos \frac{\pi }{2} - i$$\sin \frac{\pi }{2}$

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