Cube roots of a positive real constant from one complex root, roots after multiplying by i, and the area of their triangle

Let \(c\) be a positive real constant, and consider the equation \(z^3=c\) for \(z\in\mathbb{C}\).

It is known that \(z=-2+2i\sqrt3\) satisfies this equation.

1. Find the value of \(c\).[2]
2. Write down the remaining two roots of \(z^3=c\), each in the form \(a+bi\) with \(a,b\in\mathbb{R}\).[2]
3. Find every root of the equation \((iz)^3=c\), each in the form \(a+bi\) with \(a,b\in\mathbb{R}\).[2]
4. On an Argand diagram, the roots found in part (c) are plotted as the points \(A\), \(B\) and \(C\).
   Find the area of triangle \(ABC\).[2]