Solve the equation \(z ^ { 2 } + ( 2 \sqrt { } 3 ) \mathrm { i } z - 4 = 0\), giving your answers in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real.
Sketch an Argand diagram showing the points representing the roots.
Find the modulus and argument of each root.
Show that the origin and the points representing the roots are the vertices of an equilateral triangle.