Random elements in group algebras

Is it possible to get a random element of $\mathbb{C}[G]$? If not, what is the problem?

Magma doesn’t appear to like giving random elements of an infinite set (it even complains when you ask for a random integer, for example, without giving it any bounds). Instead of using ComplexField, we will use the field $\mathbb{Q}(i)$. Here is a concrete way to generate some sort of random elements group algebras:

> G := Sym(3);
> Q<i> := QuadraticField(-1);
> A := GroupAlgebra(Q,G);
> x := Random(-100,100);
> y := Random(-100,100);
> z := x+i*y;
41*i + 34

Now

> A!z*Random(G);
(41*i + 34)*(1, 2, 3)

There should be a better way to get better random elements of $\mathbb{C}[G]$. No?