Final answer:
To solve the equation for x, we rearrange the terms to isolate x on one side and then divide by the coefficient of x. The resulting equation is x = (5 - 3i)/(5 - 8y).
Step-by-step explanation:
To solve the equation -3x + 5 - 3i = 2x + 8yi, we'll first move all terms involving x to one side of the equation and combine like terms. This means adding 3x to both sides of the equation and subtracting 8yi from both sides.
After rearranging, the equation becomes: 5x = 5 - 3i - 8yi.
Now, to solve for x, we divide both sides by (5):
x = (5 - 3i - 8yi)/5
To express this in terms of y, factor out the real and imaginary parts separately. Since there's a -8yi term, we should isolate y in the denominator which gives us the solution:
x = (5 - 3i)/(5 - 8y).