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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers2 Marks
MCQ
If $(-7-24 i )^{\frac{1}{2}}=x- i y$, then $x^2+y^2=$
  • A
    15
  • ✓
    25
  • C
    $-25$
  • D
    $-15$
✓

Answer

Correct option: B.
25
(B)
$\sqrt{-7-24 i }=x- i y$
Squaring both sides, $-7-24 i =x^2-y^2- i (2 x y)$
Equating real and imaginary parts, we get
$x^2-y^2=-7$ and $2 x y=24$
$\therefore \quad x^2+y^2=\sqrt{49+576}=\sqrt{625}=25$

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