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Definition of Functions

Find the valu...

Question

Find the values of $x$ and $y$ which satisfy the equations $(x, y \in R)$
$(x + 2 y) + (2 x - 3 y) i + 4 i = 5$

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Solution

$(x + 2 y) + (2 x - 3 y) i + 4 i = 5$
$(x + 2 y) + (2 x - 3 y) i = 5 - 4 i$
Comparing the real and imaginary part of both the sides we have,
$x + 2 y = 5$
$2 x - 3 y = - 4$
$2 (x + 2 y) = 5 \times 2$
$2 x + 4 y = 10$
$\pm 2 x \mp 34 = \mp 4$
solving above equations we get,
$+ 7 y = 14$
$y = 2$
puttinh values in first equation we have,
$x + 2 \times 2 = 5$
$x + 4 = 5$
$x = 5 - 4 = 1$

So, $x = 1$ and $y = 2$

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