This thesis explores the application of complex numbers in electrical engineering, demonstrating their key role in the analysis and design of electrical systems. The paper begins with the basic definition of complex numbers and their basic operations, after which it focuses on their application in the analysis of electric circuits. Special attention is paid to the display of impedance, phase shift between voltage and current, and the analysis of complex power in AC circuits. The paper also deals with the frequency response of the system, where complex numbers enable an effective analysis of the system's behavior at different frequencies. The application of complex numbers in the analysis of electromagnetic waves, including calculations of reflection and transmission, is also covered. An important part of the work is devoted to the stability of electrical systems where the concepts of poles and zeros of transfer functions are used. The final part of the paper considers the application of complex numbers in modern electronic and electrotechnical devices, with a view to future directions of development and research. Finally, the paper emphasizes the necessity of complex numbers as a mathematical tool in modern electrical engineering and electronics, emphasizing their potential for further progress in this field.