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