solve for x and y

Question

Solve for x and y. 4x - 9i = - 8 + 3yi

Answer 1

Mike D. seems to have the correct solution, or what the answer the problem was probably intended to have.

But when you have one equation, with 2 unknowns, there're an infinite number of solutions.

For example, let x=0, then solve for y. You have -9i=-8+3yi

3yi = 8-9i, then divide by 3i

y=(8-9i)/3i =(-8/3i)-3

y=-3 - (8/3i) = -3 -(8i/-3)

y=-3 +(8/3)i

Or let y=0, then 4x-9i=-8

4x=-8+9i, divide by 4

x = -2 +9i/4 = -2 + (9/4)i

There is no unique solution, although it's common to write a complex number as the real term plus the imaginary term. So 4x would be real and 3yi the imaginary component. Then 4x=-8, x=-2 and

3yi=-9i, y=-3

But x and y could also be complex with each having a real and imaginary component. Then there are an infinite number of solutions

Answer 2

Karla

Here we just equate the real and the imaginary parts.

4x - 9i = -8 + 3yi

Real : 4x = -8, so x = -2

Imaginary : -9i = 3yi, so -9 = 3y, so y = -3

Mike