If 3x + 2iy 5i - 2 = 15 8x + 3iy , then - Vidyadip

MCQ

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

A
$x = 1,y = - 3$
B
$x = - 1,y = 3$
C
$x = 1,y = 3$
✓
$x = - 1,y = - 3$or $x = 1,$$y = 3$

✓

Answer

Correct option: D.

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

d
(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 $x = \pm 1,y = \pm 3$

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