(a) Solve the equation \(z^2 - 6iz - 12 = 0\), giving the answers in the form \(x + iy\), where \(x\) and \(y\) are real and exact.

(b) On a sketch of an Argand diagram with origin \(O\), show points \(A\) and \(B\) representing the roots of the equation in part (a).

(c) Find the exact modulus and argument of each root.

(d) Hence show that the triangle \(OAB\) is equilateral.