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

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

$\sin 4\theta $ can be written as

Let $A=\left\{(x, y) \in R ^2: y \geq 0,2 x \leq y \leq \sqrt{4-(x-1)^2}\right\}$ and $B=\left\{(x, y) \in R \times R : 0 \leq y \leq \min \left\{2 x, \sqrt{4-(x-1)^2}\right\}\right\}$ Then the ratio of the area of $A$ to the area of $B$ is

Let $PQ$ and $RS$ be the tangent at the extremities of the diameter $PR$ of a circle of radius $r$. If $PS$ and $RQ$ intersect at a point $X$ on the circumference of the circle, then $(PQ.RS)$ is equal to

Eight chairs are numbered $1$ to $8$. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked $1$ to $4$ and then men select the chairs from amongst the remaining. The number of possible arrangements is

The circle on the chord $x\cos \alpha + y\sin \alpha = p$ of the circle ${x^2} + {y^2} = {a^2}$ as diameter has the equation

$\int_{}^{} {\frac{1}{{{x^2}{{({x^4} + 1)}^{3/4}}}}dx = } $

A particle moves in a straight line with a velocity given by $\frac{{dx}}{{dt}} = x + 1$($x$ is the distance described). The time taken by a particle to traverse a distance of $99$ metre is

If $A = \left( {\begin{array}{*{20}{c}}1&2&3\\3&1&2\\2&3&1\end{array}} \right)$ and $B = \left( {\begin{array}{*{20}{c}}{ - 5}&7&1\\1&{ - 5}&7\\7&1&{ - 5}\end{array}} \right)$ then $AB$ is equal to

If the probability that a student is not a swimmer is $\frac{1}{5}$, then the probability that out of $5$ students one is swimmer is

If $k$ is a scalar and $I $ is a unit matrix of order $ 3$ , then $adj(k\,I) = $