How does the concept of impedance relate to the analysis of electrical circuits? Discuss the theoretical underpinnings of impedance, including its definition, mathematical representation, and physical significance in the context of AC circuits. Explain the distinction between resistance, inductance, and capacitance, and their respective contributions to the impedance of a circuit. Furthermore, elucidate how impedance matching techniques are employed in electrical engineering to optimize power transfer and minimize signal distortion, particularly in applications such as antenna design, audio systems, and transmission line networks.