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..?
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.