ABSTRACT
This chapter begins by describing the relation between Cartesian and polar representations of a complex number. This is followed by a section on complex exponential function, such as Euler’s formula with examples. The chapter introduces the relevant aspects of complex variables. The complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal. The chapter considers basic operations with complex numbers and the different characteristics of these numbers. It provides information on analytic functions, including Cauchy–Riemann Conditions and Cauchy Integral Formula. To show the diverse applications of the material, numerous and widely varied solved boundary value problems are also presented. The chapter concludes with Mathematica procedures to make ordinary and partial differential equations used in engineering non-dimensional.
