- A transformation \(T\) from the \(z\)-plane to the \(w\)-plane is given by
$$w = \frac { z - 1 } { z + 1 } , \quad z \neq - 1$$
The line in the \(z\)-plane with equation \(y = 2 x\) is mapped by \(T\) onto the curve \(C\) in the \(w\)-plane.
- Show that \(C\) is a circle and find its centre and radius.
The region \(y < 2 x\) in the \(z\)-plane is mapped by \(T\) onto the region \(R\) in the \(w\)-plane.
- Sketch circle \(C\) on an Argand diagram and shade and label region \(R\).
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