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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
$\big(\sqrt{-2}\big)\big(\sqrt{-3}\big)$ is equal to:
  • A
    $\sqrt{6}$
  • ✓
    $-\sqrt{6}$
  • C
    $\text{i}\sqrt{6}$
  • D
    none of these.
✓

Answer

Correct option: B.
$-\sqrt{6}$
$\sqrt{-2}\times\sqrt{-3}$
$=\sqrt{2}\times\sqrt{3}\times\sqrt{-1}\times\sqrt{-1}$
$=\sqrt{6}\times\text{i}\times\text{i}$
$=\sqrt{6}\times\text{i}^2$
$=-\sqrt{6} \ [\because\text{i}^2=-1]$

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