- The complex numbers \(z\) and \(w\) are represented, respectively, by the points \(P ( x , y )\) and \(Q ( u , v )\) in Argand diagrams and
$$w = \frac { z } { 1 - z }$$
- Show that \(v = \frac { y } { ( 1 - x ) ^ { 2 } + y ^ { 2 } }\) and obtain an expression for \(u\) in terms of \(x\) and \(y\).
- The point \(P\) moves along the line \(y = 1 - x\). Find and simplify the equation of the locus of \(Q\).