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Math Help - Complex number problem

  1. #1
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    Complex number problem

    "Let z be a complex number and z (w/ a bar over it) be its conjugate. What are the four values of z for which zz(bar) and z^2 + z(bar)^2 = 6 ?"

    I can't seem to a get an answer...I just did a lot of work and didn't get anything. I simplified it down to z^4 + 25 / z^2 = 6 and -z(bar) +6z(bar)^2 = 25, but that's all.
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  2. #2
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    Quote Originally Posted by ggeek101 View Post
    "Let z be a complex number and z (w/ a bar over it) be its conjugate. What are the four values of z for which zz(bar) and z^2 + z(bar)^2 = 6 ?"

    I can't seem to a get an answer...I just did a lot of work and didn't get anything. I simplified it down to z^4 + 25 / z^2 = 6 and -z(bar) +6z(bar)^2 = 25, but that's all.

    z=a+bi
    \bar{z}=a-bi

    z^2=a^2+2abi-b^2
    \bar{z} ^2=a^2-2abi-b^2

    z^2+\bar{z}^2=2a^2-2b^2=6

    z\bar{z}=a^2+b^2=6

    So solve a^2-b^2=3 and a^2+b^2=6
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  3. #3
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    Wow, I over thought this problem. I like your approach. Thanks!
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  4. #4
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    no problemo.... i took it further and i believe the answers are not pretty, just so you're aware
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