Given that on an Argand diagram the locus of points defined by \(| z + 5 - 12 i | = 10\) is a circle,
write down,
the coordinates of the centre of this circle,
the radius of this circle.
Show, by shading on an Argand diagram, the set of points defined by
$$| z + 5 - 12 i | \leqslant 10$$
For the set of points defined in part (b), determine the maximum value of \(| z |\)
The set of points \(A\) is defined by
$$A = \{ z : 0 \leqslant \arg ( z + 5 - 20 i ) \leqslant \pi \} \cap \{ z : | z + 5 - 12 i | \leqslant 10 \}$$
Determine the area of the region defined by \(A\), giving your answer to 3 significant figures.