Solve the following
Question:

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

(a) 9/85

(b) −9/85

(c) 53/85

(d) none of these

Solution:

(c) $\frac{53}{85}$

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

$\Rightarrow x+i y=\frac{3+5 i}{7-6 i} \times \frac{7+6 i}{7+6 i}$

$\Rightarrow x+i y=\frac{21+53 i+30 i^{2}}{49-36 i^{2}}$

$\Rightarrow x+i y=\frac{21-30+53 i}{49+36}$

$\Rightarrow x+i y=\frac{-9}{85}+i \frac{53}{85}$

On comparing both the sides :

$y=\frac{53}{85}$

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