Engineering Mathematics, Volume 2

13

Functions of a Complex Variable

13.1 Introduction

Many engineering problems can be solved using Complex Variable Theory. Some of the elementary problems dealing with applications to electric circuits or mechanical vibrating systems need only elementary knowledge of complex analysis. Advanced problems in heat conduction, fluid flow and electrostatics require knowledge of complex analysis.

Equations such as x² = −1 have no solutions in real variables. By defining as a complex unit, the system of real numbers can be extended to the complex number system.

13.2 Complex Numbers—Complex Plane

A complex number z is an ordered pair of real numbers ...