On a single Argand diagram, sketch the locus of points for which
(A) \(| z - 3 \mathrm { j } | = 2\),
(B) \(\quad \arg ( z + 1 ) = \frac { 1 } { 4 } \pi\).
Indicate clearly on your Argand diagram the set of points for which
$$| z - 3 \mathrm { j } | \leqslant 2 \quad \text { and } \quad \arg ( z + 1 ) \leqslant \frac { 1 } { 4 } \pi .$$
(A) By drawing an appropriate line through the origin, indicate on your Argand diagram the point for which \(| z - 3 j | = 2\) and \(\arg z\) has its minimum possible value.
(B) Calculate the value of \(\arg z\) at this point.