Find the real values of $x$ and $y$ , if
$(x + i y) (2 - 3 i) = 4 + i$

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Solution

$(x + i y) (2 - 3 i) = 4 + i$

$2 x - 3 i x + 2 i y + 3 y = 4 + i$

$(2 x + 3 y) + i (2 y - 3 x) = 4 + i$

Comparing both sides of the above equation,

$2 x + 3 y = 4$ (1)

And,

$2 y - 3 x = 1$ (2)

From equation (1) and (2), by elimination method,

$x = \frac{5}{13}$ and

$y = \frac{14}{13}$

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Similar questions

Q. If

(x + i y) (2 - 3 i) = 4 + i

then (x, y) =

Find the real values of x and y, if

$(i) (x + i y) (2 - 3 i) = 4 + i (i i) (3 x - 2 i y) (2 + i)^{2} = 10 (1 + i) (i i i) \frac{(1 + i) x - 2 i}{3 + i} + \frac{(2 - 3 i) y + i}{3 - i} = i (i v) (1 + i) (x + i y) = 2 - 5 i$

Q. Find the real values of x and y, if
(i)

(x + i y) (2 - 3 i) = 4 + i

(ii)

(3 x - 2 i y) (2 + i)^{2} = 10 (1 + i)

(iii)

\frac{(1 + i) x - 2 i}{3 + i} + \frac{(2 - 3 i) y + i}{3 - i}

(iv)

(1 + i) (x + i y) = 2 - 5 i

Q. If

(x + i y) (2 - 3 i) = 4 + i (\frac{1}{2})

then

x + y =

Solve:

(x + i y) (2 - 3 i) = 4 + i

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Find the real values of x and y, if (x+iy)(2−3i)=4+i

(x+iy)(2−3i)=4+i 2x−3ix+2iy+3y=4+i (2x+3y)+i(2y−3x)=4+i Comparing both sides of the above equation, 2x+3y=4 (1) And, 2y−3x=1 (2) From equation (1) and (2), by elimination method, x=513 and y=1413

Find the real values of $x$ and $y$ , if
$(x + i y) (2 - 3 i) = 4 + i$

$(x + i y) (2 - 3 i) = 4 + i$

$2 x - 3 i x + 2 i y + 3 y = 4 + i$

$(2 x + 3 y) + i (2 y - 3 x) = 4 + i$

Comparing both sides of the above equation,

$2 x + 3 y = 4$ (1)

And,

$2 y - 3 x = 1$ (2)

From equation (1) and (2), by elimination method,

$x = \frac{5}{13}$ and

$y = \frac{14}{13}$