rootof ???

[parisse]

rootof(P,Q) is used for algebraic extension representation, it is P(alpha) where Q(alpha)=0, Q being an irreducible polynomial over the rationals. You can evalf rootofs to get a numeric approximation:
approx(-1/12*rootof([[1,-3,-5,3], [1, 0, -2, 0, 9]])
In other words sqrt(i) is P(alpha) where P(x)=-1/12*(x^3-3x^2-5x+3) and alpha is root of Q(x)=x^4-2x^2+9.
rootof are created when you mix several algebraic extensions of small order (2 of order 2 in your example sqrt(2) and i).