7. A transformation from the \(z\)-plane to the \(w\)-plane is given by $$w = \frac { ( 1 + \mathrm { i } ) z + 2 ( 1 - \mathrm { i } ) } { z - \mathrm { i } } \quad z \neq \mathrm { i }$$ The transformation maps points on the imaginary axis in the \(z\)-plane onto a line in the \(w\)-plane.

1. Find an equation for this line. The transformation maps points on the real axis in the \(z\)-plane onto a circle in the \(w\)-plane.
2. Find the centre and radius of this circle.