The subject of series is one of the most important works that has always been of interest in the field of mathematics analysis and plays a fundamental role in solving complex mathematical problems. Especially the power series of complex numbers, which has significant advantages in mathematics. The purpose of this research is to investigate and understand series of complex numbers. In this research, the latest articles, theses, treatises and numerical analysis books have been used. In the numerical analysis of series of complex numbers, it is one of the most important and widely used branches. Since no comprehensive research has been done on this issue until now and most researchers have used less series of complex numbers in their research, which series of power solves many complex problems of mathematics easily, including its applications in the root of numbers. Negative are arithmetic and geometric series, Taqat and Taylor series. In this article, open and closed library pages and authentic internet articles have been used. It is worth mentioning that this article is important for all those interested in mathematics and especially for those interested in mathematics, engineering, physics and computer science, and they can use the contents of this research in their scientific and academic life. Since series in complex numbers has different branches, I have tried to include the topics of series of complex numbers in this research so that it will be a good extension for the researchers of mathematical science in the future.

This thesis addresses issues related to organizing internal audit in joint-stock companies based on national and international standards and explaining it based on international standards. Also, information on the effectiveness of the corporate governance system, which can be achieved through the effective organization of internal audit in joint-stock companies, is provided from foreign experience. As a result of the study, issues of improving the internal audit process based on international requirements were considered, and corresponding conclusions and proposals were formed.

This article describes the goal and content of the methodology of teaching music, specific (optimal) methods of teaching music and their types.

This article describes the essence of the concepts of "competence" and "professional competence", the qualities of professional competence, and the development of the professional competence of a pedagogue.

This article explores the importance and effectiveness of new teaching methods in the development of Primary School students. Modern pedagogical approaches, the use of technologies and methods aimed at the personality of the student are analyzed and their impact on the level of knowledge, creative abilities and general development of students is assessed. The results of the study show the superiority of new methods over traditional ones, and recommendations are made for improving the system of primary education in the future.