Site hosted by Angelfire.com: Build your free website today!
V.1

80 - 81

Some pecularities of derivative of complex function

line.gif (1279 bytes)

 

80

Noting the above definitions, consider some complex function f ( z ) proceeding the one-valued mapping of -vicinity of the point z0 of the complex plane Z into -vicinity of the point w0 of the complex plane W (see Fig. 1). Choose in the -vicinity of z0 two points z1(x1, y1) and z2(x2, y2). In accord with the complex function definition, some points w1(u1, v1) and w2(u2, v2) of mapping on the complex plane W correspond them. And according to the condition of one-valued mapping, if

(7)

Form the differences between the picked points z1 , w1, z2 , w2 , z0 and w0 correspondingly:

81

(8)

Noting (7), in general case

At the same time

Thus, even from the condition

generally there does not follow

Contents: / 77 - 78 / 78 - 79 / 80 - 81 / 81 - 83 / 84 - 86 / 86 - 88 /

/ 88 - 90 / 90 - 91 / 91 - 93 / 93 - 94 /