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Math Help - Addition of complex conjugates by induction

  1. #1
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    Addition of complex conjugates by induction

    prove that overbar/(z1 + z2 + .... + zn) = overbar(z1) + overbar(z2) + .... +overbar(zn)

    I showed true for n = 2 already
    I then assumed true for n = k and wrote out the induction hypothesis
    Then of course I need to show true for n = k + 1 and substitute the induction hypothesis in. So I came out with

    overbar(z1 + z2 + .... + zn + zn+1) = overbar/(z1 + z2 + .... + zn) + overbar(zn+1)

    I know I'm close, and I'm sure it's something simple that I'm missing but I don't know what to do next.

    Any help?
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  2. #2
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    Re: Addition of complex conjugates by induction

    Quote Originally Posted by Johngalt13 View Post
    prove that overbar/(z1 + z2 + .... + zn) = overbar(z1) + overbar(z2) + .... +overbar(zn)
    I showed true for n = 2 already
    I then assumed true for n = k and wrote out the induction hypothesis
    Then of course I need to show true for n = k + 1 and substitute the induction hypothesis in. So I came out with

    \overline{(z_1 + z_2 + .... + z_n + z_{n+1})} = \overline{(z_1 + z_2 + .... + z_n)} + \overline{z_{n+1}}
    You are right there.
    You know it works for two numbers as well as \overline{(z_1 + z_2 + .... + z_n)}
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  3. #3
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    Re: Addition of complex conjugates by induction

    Quote Originally Posted by Plato View Post
    You are right there.
    You know it works for two numbers as well as \overline{(z_1 + z_2 + .... + z_n)}
    Edit:Nevermind I got it, thanks that helped!
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