Show that the equation
$$\left( 2 z - z ^ { * } \right) ^ { * } = z ^ { 2 }$$
has exactly four solutions and state these solutions.
6
Plot the four solutions to the equation in part (a) on the Argand diagram below and join them together to form a quadrilateral with one line of symmetry.
\includegraphics[max width=\textwidth, alt={}, center]{8f7a5fc0-6936-4aed-a173-e221bf86e4fd-09_842_860_406_589}
6
(ii) Show that the area of this quadrilateral is \(\frac { \sqrt { 15 } } { 2 }\) square units.