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Thread: Complex number question-

  1. #1
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    Complex number question-

    If z(bar) = z , what can you say about z?


    What exactly is teh question asking us- all i can come up with is- z(bar) is basically a rotation about the x-axis at teh same argumetn as z...

    same modulus ??

    what else ?
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  2. #2
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    Quote Originally Posted by Khonics89 View Post
    If z(bar) = z , what can you say about z??
    $\displaystyle \begin{gathered}
    \overline {x + yi} = x - yi \hfill \\
    \overline {3 - 4i} = 3 + 4i \hfill \\
    \overline { - 1 - i} = - 1 + i \hfill \\
    \overline {4i} = - 4i \hfill \\
    \overline { - 7} = - 7 \hfill \\
    \end{gathered} $
    From these examples can you answer the question?
    Last edited by mr fantastic; May 25th 2009 at 01:51 AM. Reason: Updated quote with new username of OP
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    I know you get that minus sign ??
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  4. #4
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    Quote Originally Posted by Khonics89 View Post
    I know you get that minus sign ??
    The question is: "for what complex numbers is it true that $\displaystyle \overline z = z~?$"
    What sort of numbers are left unchanged by taking the conguate?
    Last edited by mr fantastic; May 25th 2009 at 01:51 AM.
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  5. #5
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    the real parts ....
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  6. #6
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    Quote Originally Posted by Khonics89 View Post
    the real parts ....
    Exactly. If $\displaystyle z = \overline z $ then $\displaystyle z$ is a real number.
    Or $\displaystyle \Im m(z) = 0$.
    Last edited by mr fantastic; May 25th 2009 at 01:52 AM.
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