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Math Help - complex numbers

  1. #1
    Senior Member
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    complex numbers

    Find the real numbers x and y if \frac{1}{x+iy}+\frac{1}{1+2i}=1

    I started like this :

    Multiply their respective conjugates for both terms :

    i got \frac{x-iy}{x^2+y^2}+\frac{1-2i}{5}=1
    continue solving from here ,

     <br />
\frac{x^2+y^2+5x}{5x^2+5y^2}-[\frac{5y+2x^2+2y^2}{5x^2+5y^2}]i=1<br />

    so i ot 2 equations here :

    5x=4x^2+4y^2

    5y+2x^2+2y^2=0

    I am not sure how to continue from here .. not even sure if my above working is correct . THanks .
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  2. #2
    MHF Contributor red_dog's Avatar
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    \left\{\begin{array}{ll}4x^2+4y^2-5x=0\\2x^2+2y^2+5y=0\end{array}\right.

    Multiply the second ecuation by 2 and substract from the first:

    -5x-10y=0\Rightarrow x=-2y

    Replace x in the second equation:

    10y^2+5y=0

    Then y_1=0\Rightarrow x_1=0 which are not good

    and y_2=-\frac{1}{2}\Rightarrow x_2=1
    Last edited by red_dog; September 11th 2009 at 10:14 AM.
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  3. #3
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    it can be done by this way
    Attached Thumbnails Attached Thumbnails complex numbers-untitled.bmp  
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