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Math Help - find all z values

  1. #1
    Member
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    Dec 2008
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    152

    find all z values

    find all values for z for the following equation:

     z^2 + 2iRe(z) = |z|

    I tried
    |z|^2 \cdot (cos 2\phi + i \cdot sin 2\phi) + 2i \cdot a = |z|

     |z| \cdot (cos 2\phi + i \cdot sin 2\phi) + \frac{2i \cdot a}{|z|} = 1

    what do i do now? can someone show me how to continue (or solve it if possible)?
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  2. #2
    Banned
    Joined
    Oct 2009
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    4,261
    Quote Originally Posted by metlx View Post
    find all values for z for the following equation:

     z^2 + 2iRe(z) = |z|

    I tried
    |z|^2 \cdot (cos 2\phi + i \cdot sin 2\phi) + 2i \cdot a = |z|

     |z| \cdot (cos 2\phi + i \cdot sin 2\phi) + \frac{2i \cdot a}{|z|} = 1

    what do i do now? can someone show me how to continue (or solve it if possible)?

    Put z = x + yi, so your equation is:

    x^2-y^2+2x(y+1)i =\sqrt{x^2+y^2}, and compare real and imaginary parts:

    ==\,\,x^2-y^2=\sqrt{x^2+y^2}
    ==\,\,2x(y+1)=0\Longrightarrow x=0\,\,or\,\,y=-1 and etc.

    Tonio
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