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Model Paper 5 — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSModel Paper 51 Mark
MCQ
If $x+i y=\frac{3+5 i}{7-6 i}$, then $y=$
  • A
    $\frac{43}{85}$
  • B
    $\frac{-9}{85}$
  • C
    $\frac{9}{85}$
  • D
    $\frac{53}{85}$
✓

Answer

(d) $\frac{53}{85}$
Explanation: $\frac{53}{85}$ 
$x + iy =\frac{3+5 i}{7-6 i}$
$\begin{array}{l}\Rightarrow x + iy =\frac{3+5 i}{7-6 i} \times \frac{7+6 i}{7+6 i} \\ \Rightarrow x + iy =\frac{21+53 i+30 i^2}{49-36 i^2} \\ \Rightarrow x + iy =\frac{21-30+53 i}{49-36 i} \\ \Rightarrow x + iy =\frac{-9}{85}+i \frac{53}{85}\end{array}$
On comparing both the sides: 
$y=\frac{53}{85}$

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