Sketch, on the Argand diagram below, the locus \(L\) of points satisfying
$$\arg ( z - 2 \mathrm { i } ) = \frac { 2 \pi } { 3 }$$
A circle \(C\), of radius 3, has its centre lying on \(L\) and touches the line \(\operatorname { Im } ( z ) = 2\). Sketch \(C\) on the Argand diagram used in part (a).
Find the centre of \(C\), giving your answer in the form \(a + b \mathrm { i }\). [0pt]
[3 marks]