Final answer:
The values of x and y that satisfy the equation 4x - 36i = -36 + 6yi are x = -9 and y = -6 by equating the real and imaginary parts respectively.
Step-by-step explanation:
To find the values of x and y that satisfy the equation 4x - 36i = -36 + 6yi, we must compare the real components and the imaginary components of both sides of the equation.
First, we identify that the real part of the left side is 4x, and the real part of the right side is -36. These must be equal for the equation to hold true, so we have 4x = -36. By dividing both sides by 4, we find that x = -9.
Next, we compare the imaginary parts. On the left side, we have -36i, and on the right side, we have 6yi. Since the coefficients of i must be the same for the equality to hold, we can equate -36 to 6y. Consequently, dividing by 6 gives us y = -6.
Therefore, the values of x and y that satisfy the given equation are x = -9 and y = -6.