Overview of Complex Analysis and Applications

This work is an exploration of complex analysis as a tool for physics and engineering. Although nothing in reality is a "complex number," it includes an overview of the topics in four investigations, and applications in the real-word. Results begin and end in real number theory, but have a path through the complex plane, which influences the result, but remains hidden. The topics also include the Laplace equation, harmonic functions, subharmonic analysis, the residue theorem, the Cauchy principle value, conformal mapping, and graphical rendering.