ABSTRACT
This chapter discusses the exponential function and its applications. It provides a natural generalization of the familiar definition of the exponential function from calculus. An immediate consequence of this new definition of the complex exponential is the complex-analytic definition of the sine and cosine functions. The complex exponential satisfies familiar rules of exponentiation. The chapter discusses different exponentiation laws, the polar form of a complex number, and the polar coordinates of a point in a plane. The properties of the exponential operation can be used together with the polar representation. Under multiplication of complex numbers, arguments are additive and moduli multiply. The chapter discusses the Cauchy—Schwarz Inequality and provides a set of exercises based on the exponential function.
