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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers2 Marks
MCQ
If $(x+y i )(3-4 i )=5+12 i$, then $\sqrt{x^2+y^2}=$
  • A
    65
  • B
    $\frac{5}{13}$
  • ✓
    $\frac{13}{5}$
  • D
    18
✓

Answer

Correct option: C.
$\frac{13}{5}$
(C)
$(3 x+4 y)+ i (-4 x+3 y)=5+12 i$
$\therefore \quad 3 x+4 y=5$ and $-4 x+3 y=12$
By solving, we get
$x=-\frac{33}{25}$ and $y=\frac{56}{25}$
$\therefore \quad \sqrt{x^2+y^2}=\frac{13}{5}$

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