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Complex Numbers and Quadratic Equations — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers and Quadratic Equations1 Mark
MCQ
If $\frac{(\text{a}^2+1)^2}{2\text{a}-\text{i}}=\text{x}+\text{iy},$ then $\text{x}^2+\text{y}^2$ is equal to:
  • ✓
    $\frac{(\text{a}^2+1)^4}{4\text{a}^2+1}$
  • B
    $\frac{(\text{a}+1)^2}{4\text{a}^2+1}$
  • C
    $\frac{(\text{a}^2-1)^2}{(4\text{a}^2-1)^2}$
  • D
    None of these
✓

Answer

Correct option: A.
$\frac{(\text{a}^2+1)^4}{4\text{a}^2+1}$
$\text{x}+\text{iy}=\frac{(\text{a}^2+1)^2}{2\text{a}-\text{i}}$
Taking modulus on both the sides, we get:
$\sqrt{\text{x}^2+\text{y}^2}=\frac{(\text{a}^2+1)^2}{\sqrt{4\text{a}^2+1}}$
Squaring both sides, we get,
$\text{x}^2+\text{y}^2=\frac{(\text{a}^2+1)^4}{{4\text{a}^2+1}}$

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