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If $\frac{3 x + 2 i y}{5 i - 2} = \frac{15}{8 x + 3 i y}$ , then

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$x = 1, y = - 3$

$x = - 1, y = 3$

$x = - 1, y = - 3 o r x = 1, y = 3$

$x = 1, y = 3$

answer is D.

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Detailed Solution

Given that $\frac{3 x + 2 i y}{5 i - 2} = \frac{15}{8 x + 3 i y}$

$\Rightarrow 24 x^{2} + 9 i x y - 6 y^{2} + 16 i x y = 75 i - 30$

$\Rightarrow 24 x^{2} - 6 y^{2} + 25 i x y = 75 i - 30$

Equating real and imaginary parts, we get

$24 x^{2} - 6 y^{2} = - 30 o r 4 x^{2} - y^{2} = - 5$ and $x y = 3$

On solving we get $x = \pm 1, y = \pm 3$

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