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Math Help - Solving a system of complex numbers

  1. #1
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    Solving a system of complex numbers

    I can't seem to figure out this system of complex numbers, the method I am trying is taking way too long. Is there any quicker way? (doing it by hand, solving for X and Y)

    \frac{X}{10} + \frac{X-Y}{5 + 15i} = 1

    \frac{Y}{-10i} + \frac{Y-X}{5+15i} = 0.866+0.5i

    EDIT: Sorry this probably should have gone in Linear Algerba
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  2. #2
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    anyone?
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  3. #3
    Member Ruun's Avatar
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    This is a linear equation for some x,y \in \mathbb{C} so you know that the solution will be a line, this is, the solution will have dimension 1 (why?). Now, solving
    <br />
\frac{x(5+15i)+10x-10y}{10(5+15i)}=1

    \frac{x(15+15i)-10y}{10(5+5i)}=1

    x(15+15i)-10y=10(5+5i)

    x=\frac{10(5+5i)+10y}{15+15i}
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