5 The complex number $z$ satisfies the relation

$$| z + 4 - 4 i | = 4$$

(a) Sketch, on an Argand diagram, the locus of $z$.\\
(b) Show that the greatest value of $| z |$ is $4 ( \sqrt { 2 } + 1 )$.\\
(c) Find the value of $z$ for which

$$\arg ( z + 4 - 4 \mathrm { i } ) = \frac { 1 } { 6 } \pi$$

Give your answer in the form $a + \mathrm { i } b$.

\hfill \mbox{\textit{AQA FP2  Q5}}