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

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4-1.Complex numbers

medium

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

$x = 1,y = - 3$

$x = - 1,y = 3$

$x = 1,y = 3$

$x = - 1,y = - 3$or $x = 1,$$y = 3$

Solution

(d) Given that $\frac{{3x + 2iy}}{{5i – 2}} = \frac{{15}}{{8x + 3iy}}$
==> $24{x^2} + 9ixy – 6{y^2} + 16ixy = 75i – 30$
==> $24{x^2} – 6{y^2} + 25ixy = 75i – 30$
Equating real and imaginary parts, we get
$24{x^2} – 6{y^2} = – 30$or $4{x^2} – {y^2} = – 5$and $xy = 3$
On solving we get $x = \pm 1,y = \pm 3$