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

Question 432413: how do you find real numbers x and y for which (x+2i)(y-i)=-4-7i
Answer by Gogonati(855) (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:
, simplify
, (as you know i^2=-1)
, As we know two complex numbers are equal if and only if their real parts and imaginary parts are equal.Thus, we write:
, rewrite the system
, solve the first equation
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).

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