find the equation of the right bisector of the line joining the points Z1 and Z2?

Question

Z1 and Z2 represent complex nos

Answer 1

Let z1 = x1 + iy1, z2 = x2 + iy2.
The midpoint, say P, of the line segment joining z1 and z2 has coordinates: ((x1+x2)/2 , (y1+y2)/2).
The slope, say m, of the line segment joining z1 and z2 is (y1-y2)/(x1-x2).

The reqd. perpendicular bisector passes through P and has slope -1/m.
Thus the reqd. equation is
y - (y1 + y2)/2 = {(x1 - x2)/(y1 - y2)}[x - (x1 + x2)/2]
or (2y - y1 - y2)(y1 - y2) = (2x - x1 - x2)(x1 - x2)

Answer 2

The right bisector consists of all the points which are equidistant from the two points. So one form of the equation is

mod(z - z1) = mod(z - z2)

where mod( x + iy ) is the square root of (x^2 + y^2)