Draw on an Argand diagram the locus \(L\) of points satisfying the equation \(\arg z = \frac { \pi } { 6 }\).
(1 mark)
A circle \(C\), of radius 6, has its centre lying on \(L\) and touches the line \(\operatorname { Re } ( z ) = 0\).
Draw \(C\) on your Argand diagram from part (a).
Find the equation of \(C\), giving your answer in the form \(\left| z - z _ { 0 } \right| = k\).
The complex number \(z _ { 1 }\) lies on \(C\) and is such that \(\arg z _ { 1 }\) has its least possible value. Find \(\arg z _ { 1 }\), giving your answer in the form \(p \pi\), where \(- 1 < p \leqslant 1\).