Abstract. 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.