- A complex number \(z\) is represented by the point \(P\) on an Argand diagram.
Given that
$$\arg \left( \frac { z - 4 - i } { z - 2 - 7 i } \right) = \frac { \pi } { 2 }$$
- sketch the locus of \(P\) as \(z\) varies,
- determine the exact maximum possible value of \(| z |\)