(i) Find the roots of the equation

\(z^2 + (2\sqrt{3})z + 4 = 0\),

giving your answers in the form \(x + iy\), where \(x\) and \(y\) are real.

(ii) State the modulus and argument of each root.

(iii) Showing all your working, verify that each root also satisfies the equation

\(z^6 = -64\).