Question

Solve for x and y:
(i) (3x-7)+2iy=-5y+(5+x)i
(ii) (x+iy)(2-3i)=4+i

Answer 1

(i) The given equation is

(3x-7)+2iy=-5y+(5+x)i

Equating the real parts and the imaginary parts of the given equation separately, we get

3x-7=-5y and 2y=5+x

$\Rightarrow 3x+5y=7$ and $x-2y=-5$

$x=-1$ and $y=2$ [On solving 3x+5y=7, x-2y=-5]

Hence, x=-1 and y=2.

(ii) The given equation is

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

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

$\Rightarrow 2x+3y=4$ and $2y-3x=1$ [equating real parts and imaginery parts separately]

$\Rightarrow 2x+3y=4$ and $-3x+2y=1$

$\Rightarrow x=\frac{5}{13}$ and $y=\frac{14}{13}$ [On solving 2x+3y=4, -3x+2y=1].

Hence, $x=\frac{5}{13}$ and $y=\frac{14}{13}$ is the required solution.