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Math Help - Complex Numbers

  1. #1
    Junior Member
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    Complex Numbers

    Show that z = x + iy is pure imaginary if and only if \overline z = -z

    z = x +iy
    - z = -x - iy

    \overline z = x - iy

    x - iy = -x - iy
    x = -x

    Umm...yeah I don't know how this works. Can someone help?
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  2. #2
    Super Member
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    Sorry my mistake before editing.

    From where you left off...

    2x = 0.

    Therefore x = 0

    So the value of x (the real part) is 0 for z. So z must be imaginary if -z = z's conjugate.
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