6 Throughout this question, the complex number \(z\) satisfies \(\left| z - z _ { 0 } \right| \leq \sqrt { 2 }\), where \(z _ { 0 } = 3 - \mathrm { i }\).
- Draw an Argand diagram to illustrate the locus of \(z\).
- In this question you must show detailed reasoning.
Show that the greatest possible argument of \(z\) can be written as \(\tan ^ { - 1 } \left( \frac { 1 } { n } \right)\), where \(n\) is a positive integer to be determined and \(\arg z \in ( - \pi , \pi ]\).