Date: Sep 26, 2011 8:27 PM
Author: Brad Cooper
Subject: Complex Numbers - Argand Diagram Question

Complex Numbers - Argand Diagram Question

In Gow's book, A Course in Pure Mathematics, I have managed to answer all of
the complex number questions in Chapter 6 except question 21.

21. If the complex numbers z_1, z_2, z_3 are connected by the relation

2/z_1 = 1/z_2 + 1/z_3

show that the points Z1, Z2, Z3 representing them in an Argand diagram lie
on a circle passing through the origin.

Note: _1, _2, _3 denote subscripts.

I have tried algebraic and geometrical approaches. One attempt was to show
that the three points, along with the origin, form a cyclic quadrilateral.

I used a CAS to draw a diagram for the problem, but after many hours I don't
seem to be any closer to finding a solution.

Any help much appreciated.