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Math Help - Complex conjugate

  1. #1
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    Complex conjugate

    Suppose z e C (z is an element of the complex numbers)

    Let z = x + yi with x,y e R.

    Let (z) = x - yi with x,y e R.

    Prove: (z) = z if and only if z is a real number.

    I'm having trouble with this proof in both directions. Thanks for any help.
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  2. #2
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    Quote Originally Posted by jzellt View Post
    Suppose z e C (z is an element of the complex numbers)

    Let z = x + yi with x,y e R.

    Let (z) = x - yi with x,y e R.

    Prove: (z) = z if and only if z is a real number.

    I'm having trouble with this proof in both directions. Thanks for any help.
    If z is real then y = 0 and it is trivially seen that z = (z).

    If (z) = z then x = x and y = -y => y = 0 => z is real.
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