3 It is given that \(z = - \sqrt { 3 } + \mathrm { i }\).
- Express \(z ^ { 2 }\) in the form \(r \mathrm { e } ^ { \mathrm { i } \theta }\), where \(r > 0\) and \(- \pi < \theta \leqslant \pi\).
- The complex number \(\omega\) is such that \(z ^ { 2 } \omega\) is real and \(\left| \frac { z ^ { 2 } } { \omega } \right| = 12\).
Find the two possible values of \(\omega\), giving your answers in the form \(R \mathrm { e } ^ { \mathrm { i } \alpha }\), where \(R > 0\) and \(- \pi < \alpha \leqslant \pi\).