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Math Help - complex numbers proof help

  1. #1
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    complex numbers proof help

    please can somebody help with this proof. It goes like this:
    |2-z| = |z| if and only if Re z = 1

    where z = a + bi

    any help would be greatly appreciated.
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  2. #2
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    Quote Originally Posted by riptorn70 View Post
    please can somebody help with this proof. It goes like this:
    |2-z| = |z| if and only if Re z = 1

    where z = a + bi

    any help would be greatly appreciated.

    From your definition  z = 1 + bi

    Now find |2-z| = |2-(1 + bi)| = |1 - bi| = \sqrt{1^2+(-b)^2}=\dots

    and |z| = |1 + bi| = \sqrt{1^2+(b)^2}=\dots
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  3. #3
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    Quote Originally Posted by riptorn70 View Post
    please can somebody help with this proof. It goes like this:
    |2-z| = |z| if and only if Re z = 1

    where z = a + bi

    any help would be greatly appreciated.
    Geometrically, the locus of |2-z| = |z| is the perpendicular bisector of the line segment joining z = 2 and z = 0. This is obviously the line x = 1, that is, Re(z) = 1.
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  4. #4
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    Thank you dearly Mr Fantastic for your help.
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