- (a) Shade on an Argand diagram the set of points
$$\{ z \in \mathbb { C } : | z - 4 i | \leqslant 3 \} \cap \left\{ z \in \mathbb { C } : - \frac { \pi } { 2 } < \arg ( z + 3 - 4 i ) \leqslant \frac { \pi } { 4 } \right\}$$
The complex number \(w\) satisfies
$$| w - 4 \mathrm { i } | = 3$$
(b) Find the maximum value of \(\arg w\) in the interval \(( - \pi , \pi ]\).
Give your answer in radians correct to 2 decimal places.