with rational coefficients (in other words, if "α" is algebraic), the dimension is finite. More precisely, it equals the degree of the minimal polynomial having α as a root. For example, the complex numbers C are a two-dimensional real vector space, generated by 1 and the imaginary unit "i". The latter satisfies "i"2 + 1 = 0, an equation of degree two. Thus, C is a two-dimensional R-vector space (and, as any field, one-dimensional as a vector space over itself, C). If "α" is not algebraic, the dimension of Q("α") over Q is infinite. For example, for "α" = π there is no such equation. That is, π is transcendental.