8. The transformation \(T\) from the \(z\)-plane to the \(w\)-plane is given by $$w = \frac { z + 3 \mathrm { i } } { 1 + \mathrm { i } z } , \quad z \neq \mathrm { i }$$ The transformation \(T\) maps the circle \(| z | = 1\) in the \(z\)-plane onto the line \(l\) in the \(w\)-plane.

1. Find a cartesian equation of the line \(l\). The circle \(| z - a - b \mathrm { i } | = c\) in the \(z\)-plane is mapped by \(T\) onto the circle \(| w | = 5\) in the \(w\)-plane.
2. Find the exact values of the real constants \(a\), \(b\) and \(c\).
   

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