Complex Analysis Geometry

Can someone help me with this following question which I have a lot of trouble with?

Thanks!

The aim of this question is to describe, given two complex numbers representing two vertices of a square, how to find two complex numbers representing the other two vertices of the square.

(a) Show carefully, that if z represents the point http://www.sosmath.com/CBB/latexrend...0c9a0fdaaa.gif on the complex

plane then http://www.sosmath.com/CBB/latexrend...5a60df0e2c.gif represents a point http://www.sosmath.com/CBB/latexrend...319e541aee.gif with http://www.sosmath.com/CBB/latexrend...dc0906f569.gifand http://www.sosmath.com/CBB/latexrend...793b3fa9d2.gif perpendicular to http://www.sosmath.com/CBB/latexrend...d2b6f87390.gif.

(b) If the given complex numbers http://www.sosmath.com/CBB/latexrend...b808451dd7.gif and http://www.sosmath.com/CBB/latexrend...e77c0c5d68.gif represent two adjacent vertices of the square, there are two possibilities for the pair of

complex numbers representing the other two vertices. What are

they? (And, of course, give a careful justification).

(c) If the given complex numbers http://www.sosmath.com/CBB/latexrend...b808451dd7.gif and http://www.sosmath.com/CBB/latexrend...e77c0c5d68.gif represent two diagonally opposite vertices of the square what is the pair of complex numbers

representing the other two vertices?