Question

Find the value of $x$ and $y$, if $(x+2y)+i(2x-3y)$ is the conjugate of $5+4i$.

Answer 1

Here conjugate of 5+4i is 5-4i

and (a+2y)+i(2x-3y) is the conjugate of 5+4i

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

comparing real parts and imaginary parts we get

x+2y=5 and 2x-3y=-4 _________ (1)

$\Rightarrow x=5-2y$

substituting value of x is (ii), we get

2(5-2y)-3y=-4

10-4y-3y=-4

$\Rightarrow 7y=14$

$\Rightarrow y=2$.

from (1), x=5-2(2)=5-4

$\therefore x=1$

since x=1, y=2.