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Engineering Mathematics
book

Engineering Mathematics

by Babu Ram
June 2009
Intermediate to advanced content levelIntermediate to advanced
1100 pages
42h 22m
English
Pearson India
Content preview from Engineering Mathematics

14

Functions of Complex Variables

In this chapter, we deal with functions of complex variables which are useful in evaluating a large number of new definite integrals, the theory of differential equations, the study of electric fields, thermodynamics, and fluid mechanics.

14.1 BASIC CONCEPTS

Definition 14.1.    A complex number z is an ordered pair (x, y) of real numbers x and y.

If z = (x, y) and w = (u, v) are two complex numbers, then their addition and multiplication are defined as

 

z + w = (x, y) + (u, v) = (x + u, y + v)
zw = (x, y) (u, v) = (xu – yv, xv + yu).

 

With these operations of addition and multiplication, the complex numbers satisfy the same arithmetic properties as do the real numbers.

If we write the real number x as (x

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Publisher Resources

ISBN: 9789332515611