Find the roots of the equation
$$z ^ { 2 } + ( 2 \sqrt { } 3 ) z + 4 = 0$$
giving your answers in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real.
State the modulus and argument of each root.
Showing all your working, verify that each root also satisfies the equation
$$z ^ { 6 } = - 64$$