Abstract
This article explores the integrity of mathematical knowledge in the continuous mathematical education system using complex number algebra. The research aims to prove the theorems of planimetry and identify the role of complex number algebra in solving nonstandard and olympiad problems of various complexities. The methodology is based on the application of complex number algebra to solve planimetric problems, which enhances students' interest in mathematics and fosters their cognitive activity, critical and analytical thinking. The research results demonstrate the effectiveness of complex number algebra in solving planimetric problems. The article presents examples where the application of complex number algebraic methods yielded excellent results in solving various problems. Thus, the article confirms the importance and relevance of studying complex number algebra in the context of modern educational needs and requirements for mathematical education. The significance of this research lies in enriching the methodology of mathematics teaching, particularly in the field of planimetry, and shows how the application of complex number algebra can contribute to students' improved understanding of mathematical concepts. Moreover, this study reaffirms the role of mathematics in everyday life and various professions, where mathematical knowledge and skills are essential. Thus, the article contributes to the development of education and society, highlighting the importance of in-depth study of mathematics and its application in various fields of knowledge and practice.