Indicate on an Argand diagram the set of points \(z\) for which \(| z - ( - 8 + 15 \mathrm { j } ) | < 10\).
Using the diagram, show that \(7 < | z | < 27\).
Mark on your Argand diagram the point, \(P\), at which \(| z - ( - 8 + 15 \mathrm { j } ) | = 10\) and \(\arg z\) takes its maximum value. Find the modulus and argument of \(z\) at \(P\).