SOLUTION: how do you find real numbers x and y for which (x+2i)(y-i)=-4-7i

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Question 432413: how do you find real numbers x and y for which (x+2i)(y-i)=-4-7i
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
To find the real numbers x and y, we first expand the left side of equality:
x%2Ay-x%2Ai%2B2y%2Ai-2%2Ai%5E2=-4-7i, simplify
x%2Ay-%28x-2y%29%2Ai%2B2=-4-7i, (as you know i^2=-1)
x%2Ay%2B2-%28x-2y%29%2Ai=-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%28x%2Ay%2B2=-4%2C+x-2y=7%29, rewrite the system
system%28%287%2B2y%29%2Ay=-6%2C+x=7%2B2y%29, solve the first equation
2y%5E2%2B7y%2B6=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).