Math Help - complex numbers proof help

1. 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.

2. Originally Posted by riptorn70
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 $|z| = |1 + bi| = \sqrt{1^2+(b)^2}=\dots$

3. Originally Posted by riptorn70
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.

4. Thank you dearly Mr Fantastic for your help.