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4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
The modulus and amplitude of $\frac{{1 + 2i}}{{1 - {{(1 - i)}^2}}}$ are
  • A
    $\sqrt 2 {\rm{ and }}\frac{\pi }{6}$
  • ✓
    $1$ and $0$
  • C
    $1$ and $\frac{\pi }{3}$
  • D
    $1$ and $\frac{\pi }{4}$
✓

Answer

Correct option: B.
$1$ and $0$
b
(b) $\frac{{1 + 2i}}{{1 - {{(1 - i)}^2}}} = \frac{{1 + 2i}}{{1 - (1 - 1 - 2i)}} = \frac{{1 + 2i}}{{1 + 2i}} = 1 + 0i$
Modulus $=1$
Amplitude $\theta $=${\tan ^{ - 1}}\frac{0}{1} = 0$.

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