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Math Help - algebra complex

  1. #1
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    algebra complex

    Hey guys,

    I need to find the complex solution to this: (and I apologise for not using the tools to display this stuff properly, but i havent learnt them yet and am in a hurry).

    Find complex solutions of:
    3|z|^2 + z[with a bar on it]^2 + 2z = 0
    I have no idea how to go about doing this one Ive never even seen anything like that.

    Also, {z [is a member of] C | z = z[with a bar on it]}
    Does this just mean the real number line, ie y = 0, because the only time a complex number can equal its conjugate is when it =s 0?

    Thanks a lot.
    Last edited by Flay; March 25th 2009 at 05:09 AM.
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  2. #2
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    Quote Originally Posted by Flay View Post
    Hey guys,

    I need to find the complex solution to this: (and I apologise for not using the tools to display this stuff properly, but i havent learnt them yet and am in a hurry).

    Find complex solutions of:
    3|z|^2 + z[with a bar on it]^2 + 2z = 0
    I have no idea how to go about doing this one Ive never even seen anything like that.

    Also, {z [is a member of] C | z = z[with a bar on it]}
    Does this just mean the real number line, ie y = 0, because the only time a complex number can equal its conjugate is when it =s 0?

    Thanks a lot.
    Let z = x + iy \Rightarrow \overline{z} = x - iy. Then your equation becomes:

    (4x^2 + 2y^2 + 2x) + i(2xy + 2y) = 0.

    Therefore:

    Equate real parts: 2x^2 + y^2 + x = 0 .... (1)

    Equate imaginary parts: xy + y = 0 .... (2)

    Solve equations (1) and (2) simultaneously.
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  3. #3
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    thanks very much for that
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