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STD 11 - 4.1 complex nubers — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 4.1 complex nubers1 Mark
MCQ
If ${( - 7 - 24i)^{1/2}} = x - iy,$ then ${x^2} + {y^2} = $
  • A
    $15$
  • ✓
    $25$
  • C
    $-25$
  • D
    None of these
✓

Answer

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

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