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4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
Modulus of $\left( {\frac{{3 + 2i}}{{3 - 2i}}} \right)$ is
  • ✓
    $1$
  • B
    $1/2$
  • C
    $2$
  • D
    $\sqrt 2 $
✓

Answer

Correct option: A.
$1$
a
(a)$\left( {\frac{{3 + 2i}}{{3 - 2i}}} \right) = \left( {\frac{{3 + 2i}}{{3 - 2i}}} \right)\left( {\frac{{3 + 2i}}{{3 + 2i}}} \right)$$ = \frac{{9 - 4 + 12i}}{{13}} = \frac{5}{{13}} + i\left( {\frac{{12}}{{13}}} \right)$
Modulus =$\sqrt {{{\left( {\frac{5}{{13}}} \right)}^2} + {{\left( {\frac{{12}}{{13}}} \right)}^2} = 1} $.

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