If x+i y=3+5 i 7-6 i , then y= - Vidyadip

MCQ

If $x+i y=\frac{3+5 i}{7-6 i}$, then $y=$

A
$\frac{43}{85}$
B
$\frac{-9}{85}$
C
$\frac{9}{85}$
✓
$\frac{53}{85}$

✓

Answer

Correct option: D.

$\frac{53}{85}$

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

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