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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers2 Marks
MCQ
Modulus of $\left(\frac{3+2 i}{3-2 i}\right)$ is
  • ✓
    1
  • B
    $\frac{1}{2}$
  • C
    2
  • D
    $\sqrt{2}$
✓

Answer

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

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