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Math Help - Complex numbers question

  1. #1
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    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..?
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  2. #2
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    Quote Originally Posted by blackdragon190 View Post
    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}<br />
  x - y = 5 \hfill \\<br />
  x + y - 1 = 2 \hfill \\ <br />
\end{gathered}  \right.
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  3. #3
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    Thanks But how did you get those equations?
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  4. #4
    Senior Member eumyang's Avatar
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    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.
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  5. #5
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    Oh, I get it now. Thanks!
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