(a)[3]
Solve $z^2 - 6iz - 12 = 0$, with answers expressed as $x + iy$, where $x$ and $y$ are exact real numbers.
(b)[1]
On a sketch of an Argand diagram with origin $O$, indicate points $A$ and $B$ to represent the roots from part (a).
(c)[3]
Find the exact modulus and argument for each root.
(d)[1]
Therefore show that triangle $OAB$ is equilateral.