Thread: Complex numbers question

I'm completely stuck on this one question:

Find real x and y for which x - y +2(x + y - 1)i = 5 + 4i

Can someone go through it with me or give me a hint..?

Originally Posted by blackdragon190

Findd real x and y for which x - y +2(x + y - 1)i = 5 + 4i[/I]
Can someone go through it with me or give me a hint..?

Solve this system:

Thanks But how did you get those equations?

You equate the real and imaginary parts of the 2 complex numbers. If you look at

On the left side, x - y is the real part (no i), and on the right side, 5 is the real part. So you set them equal to each other:


Look at the imaginary parts. On the left side you have 2(x + y - 1), and on the right side you have 4. So they're equal:


You can simplify a little bit by dividing both sides by 2:


So now you have the system that Plato wrote above.

Oh, I get it now. Thanks!