5 The complex number \(z\) satisfies the relation
$$| z + 4 - 4 i | = 4$$
- Sketch, on an Argand diagram, the locus of \(z\).
- Show that the greatest value of \(| z |\) is \(4 ( \sqrt { 2 } + 1 )\).
- Find the value of \(z\) for which
$$\arg ( z + 4 - 4 \mathrm { i } ) = \frac { 1 } { 6 } \pi$$
Give your answer in the form \(a + \mathrm { i } b\).