Abstract
The study aims to develop an effective methodology for teaching the topic of “Complex Numbers” in higher education institutions. The relevance of the topic is determined by the widespread use of complex numbers in various branches of mathematics, which necessitates a systematic and accessible approach to their study. In the article, the authors provide a geometric justification for the necessity of extending the set of real numbers, demonstrating the logic behind introducing complex numbers as ordered pairs. It is proven that the subset of complex numbers corresponding to points on the abscissa axis can be identified with the set of real numbers, while numbers located on the ordinate axis are interpreted as purely imaginary. Based on this, the algebraic form of a complex number is derived. The proposed method of sequential presentation of the material is intended to enhance the accessibility of the topic for students and promotes their deeper understanding of complex numbers. To enhance topic mastery, artificial intelligence tools have been integrated into lectures and practical sessions. The incorporation of artificial intelligence elements into a subject topic is not merely a methodology for theoretical presentation but also enhances the learning experience, making it interactive, personalized, and modern.