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Math Help - complex number problem

  1. #1
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    complex number problem

    solve for x and y:
    x + yi = 2/3+i + 3/2+i
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by hyzlemon View Post
    solve for x and y:
    x + yi = 2/3+i + 3/2+i
    Combine the imaginary and real parts on the right hand side:

    x + y i = (2/3 + 3/2) + 2 i

    y = 2

    and

    x = ...

    Good luck!
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  3. #3
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    Quote Originally Posted by hyzlemon View Post
    solve for x and y:
    x + yi = 2/3+i + 3/2+i
    Is the problem x+yi=\frac{2}{3+i}+\frac{3}{2+i}?
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  4. #4
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    Hello, hyzlemon!

    Solve for x and y: . x + yi \:=\: \frac{2}{3+i} +  \frac{3}{2+i}

    Rationalize the right side:

    . . \frac{2}{3+i}\cdot{\color{blue}\frac{3-i}{3-i}} + \frac{3}{2+i}\cdot{\color{blue}\frac{2-i}{2-i}} \;=\;\frac{2(3-i)}{9+1} + \frac{3(2-i)}{4+1} \;=\;\frac{6-2i}{10} + \frac{6-3i}{5}

    . . . =\;\frac{6-2i}{10} + \frac{12-6i}{10} \;=\;\frac{18-8i}{10} \;=\;\frac{9}{5} - \frac{4}{5}i


    Therefore: . x + yi \;=\;\frac{9}{5} - \frac{4}{5}i \quad\Rightarrow\quad \begin{Bmatrix}x &=& \dfrac{9}{5} \\ \\[-3mm] y &=& \text{-}\dfrac{4}{5} \end{Bmatrix}

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