2

Functions of a Complex Variable

2.1 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 i = images as a complex unit, the system of real numbers can be extended to the complex number system.

2.2 Complex Numbers-Complex Plane

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

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