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If a complex converges, then it's conjugate converges.

  1. Jan 27, 2009 #1
    1. The problem statement, all variables and given/known data

    Prove that z_n -> z_0 if and only if ~(z_n) -> ~(z_0) as n goes to infiinity.

    ~(z_n) is the conjugate of z_n.

    2. Relevant equations

    3. The attempt at a solution

    |~(z_n) - ~(z_0) | = | ~(z_n) + ~(-z_0)| <=

    |~(z_n)| + |~(-z_0) | = |z_n| + |z_0| <=

    and I can't come up with much else. It's about the same for the other direction as well.
  2. jcsd
  3. Jan 27, 2009 #2


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    Homework Helper

    Using a '*' for complex conjugation is more usual than '~'. |z*|=|z|.
    |z_n*-z_0*|=|(z_n-z_0)*|=|z_n-z_0|. Use stuff like that. Now write it in the form of a proof about limits.
  4. Jan 27, 2009 #3
    * looks better after seeing it. I just couldn't think of a way the first time around.
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