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

MCQ

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

A
$\frac{9}{85}$
B
$\frac{-9}{85}$
✓
$\frac{53}{85}$
D
none of these

✓

Answer

Correct option: C.

$\frac{53}{85}$

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

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