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4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
Amplitude of $\left( {\frac{{1 - i}}{{1 + i}}} \right)$ is
  • ✓
    $-\pi\over2$
  • B
    $\pi\over2$
  • C
    $\pi\over4$
  • D
    $\pi\over6$
✓

Answer

Correct option: A.
$-\pi\over2$
a
(a)$\left( {\frac{{1 - i}}{{1 + i}}} \right) = \frac{{1 - i}}{{1 + i}} \times \frac{{1 - i}}{{1 - i}} = \frac{{{{(1 - i)}^2}}}{2} = \frac{{ - 2i}}{2} = - i$
${\mathop{\rm Im}\nolimits} (z) < 0$, Hence amplitude =$ - \pi /2$.

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