What are the applications of complex analysis in engineering?

Complex analysis has several important applications in engineering, particularly in fields like electrical engineering, fluid dynamics, and control theory. In electrical engineering, it is used to analyze AC circuits and to understand impedance and phasors. In fluid dynamics, complex functions help model potential flow and analyze fluid behavior around objects. Additionally, control theory utilizes complex analysis in the stability analysis of systems through techniques like the Nyquist and Bode plots.