Abstract:Extension of fields is an important research content.Based on the existing fields, by the method of extension, new fields can be constructed.The understanding of number for people is the process of the extension of number fields.Algebraic extension can expand rational number field to real number field, real number field with the imaginary unit can be extended to complex field, and finite extension and algebraic extension have important connection.Based on the basic properties of the finite extension and algebraic extension, this paper researches the process of the extension of the real number field to the complex field.