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.