Question

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

Answer 1

$(x+2y)+(2x-3y)i+4i=5$

$(x+2y)+(2x-3y)i=5-4i$

The above two complex numbers are equal, so their real and imaginary parts will be equal.

$\Rightarrow x+2y=5$ ................... (1)

and

$2x-3y=-4$ .................... (2)

Multiply equation (1) with $2$,

$2x+4y=10$ .................... (3)

Subtract equation (2) from (3),

$2x+4y-2x+3y=10-(-4)$

$7y=14$

$y=2$

From equation (1),

$x=5-2y$

$x=5-4=1$

$\therefore x=1andy=2$