1.
$$z = 2 - 3 \mathrm { i }$$
- Show that \(z ^ { 2 } = - 5 - 12 \mathrm { i }\).
Find, showing your working,
- the value of \(\left| z ^ { 2 } \right|\),
- the value of \(\arg \left( z ^ { 2 } \right)\), giving your answer in radians to 2 decimal places.
- Show \(z\) and \(z ^ { 2 }\) on a single Argand diagram.