Question 432413
To find the real numbers x and y, we first expand the left side of equality:

{{{x*y-x*i+2y*i-2*i^2=-4-7i}}}, simplify

{{{x*y-(x-2y)*i+2=-4-7i}}}, (as you know i^2=-1)

{{{x*y+2-(x-2y)*i=-4-7i}}}, As we know two complex numbers are equal if and only if their real parts and imaginary parts are equal.Thus, we write:

{{{system(x*y+2=-4, x-2y=7)}}}, rewrite the system

{{{system((7+2y)*y=-6, x=7+2y)}}}, solve the first equation

{{{2y^2+7y+6=0}}} and find y=-2 and y=-3/2 Substitute and find values of x

 x=7+2*(-2)=3 and x=7+2*(-3/2)=4, thus, we have two solution, there are:

((3,-2) and (4, -3/2).