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..?

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- Aug 3rd 2010, 04:09 AMblackdragon190Complex 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..? - Aug 3rd 2010, 04:27 AMPlato
- Aug 3rd 2010, 05:11 AMblackdragon190
Thanks :) But how did you get those equations?

- Aug 3rd 2010, 05:34 AMeumyang
You equate the real and imaginary parts of the 2 complex numbers. If you look at

$\displaystyle x - y + 2(x + y - 1)i = 5 + 4i$

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:

$\displaystyle x - y = 5$

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:

$\displaystyle 2(x + y - 1) = 4$

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

$\displaystyle x + y - 1 = 2$

So now you have the system that Plato wrote above. - Aug 3rd 2010, 02:24 PMblackdragon190
Oh, I get it now. Thanks!