 Henceforth, we will suppress the injective homomorphism and assume that we are dealing with actual subfields.The field of complex numbers formula_6 is an extension field of the field of real numbers formula_7 and formula_8 in turn is an extension field of the field of rational numbers formula_9 Clearly then, formula_10 is also a field extension.We have formula_11 because formula_12 is a basis, so the extension formula_13 is finite.