Answer: Option A; x = 5, y = -13
Step-by-step explanation:
We have the equation:
(x + yi) + (4+9i) = 9-4i
Solving the left side we have:
x + y*i + 4 + 9*i = 9 - 4*i
(x + 4) + (y + 9)*i = 9 - 4*i
The real part is x + 4, and this must be equal to the real part in the right that is 9, then:
x + 4 = 9
x = 9 - 4 = 5
x = 5
And the imaginary part in the left needs to be equal to the imaginary part in the right, then:
y + 9 = -4
y = -4 - 9 = -13
y = -13
then the solution is x = 5, y = -13
The correct option is A
