Express each of the following in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real and exact:
(a) \(z + 2 z ^ { * }\);
(b) \(\frac { z ^ { * } } { \mathrm { i } z }\).
On a sketch of an Argand diagram with origin \(O\), show the points \(A\) and \(B\) representing the complex numbers \(z ^ { * }\) and \(\mathrm { i } z\) respectively. Prove that angle \(A O B\) is equal to \(\frac { 1 } { 6 } \pi\).