Final answer:
Complex analysis is a branch of mathematics that has applications in both mathematics and engineering. In mathematics, it is used to study functions of complex variables, while in engineering, it is applied in areas like electromagnetic theory, fluid dynamics, and signal processing.
Step-by-step explanation:
Complex analysis has applications in both mathematics and engineering problem-solving. In mathematics, complex analysis is used to study functions of complex variables and their properties. It helps solve problems related to conformal mappings, complex integrals, and complex differentiation. In engineering, complex analysis is applied in various areas such as electromagnetic theory, fluid dynamics, and signal processing. For example, in electrical engineering, complex analysis is used to analyze and design circuits with alternating current (AC) signals.