# Thread: Complex numbers question

1. ## 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..?

2. 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: $\left\{ \begin{gathered}
x - y = 5 \hfill \\
x + y - 1 = 2 \hfill \\
\end{gathered} \right.$

3. Thanks But how did you get those equations?

4. You equate the real and imaginary parts of the 2 complex numbers. If you look at
$x - y + 2(x + y - 1)i = 5 + 4i$
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:
$x - y = 5$

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:
$2(x + y - 1) = 4$

You can simplify a little bit by dividing both sides by 2:
$x + y - 1 = 2$

So now you have the system that Plato wrote above.

5. Oh, I get it now. Thanks!