Introduction to Complex Numbers, the History of Complex Numbers and the Complex Field

This book begins by introducing the reader to four killer applications of complex numbers through examples, two from mathematics, one from physics and one from electronics. Then the fascinating history of complex numbers is detailed including the roles of Del Ferro, Tartaglia, Cardano & Bombelli. Then in the third chapter, the complex field is discussed including the complex plane, conjugate numbers, the polar form of complex numbers, multiplication and division in polar form. powers, roots, review examples, topological aspects of the complex plane, stereographic projection, the point at infinity, and curves and regions in the complex plane. The book concludes with an exercise set.