20.1 Complex Functions as Mappings


In Chapter 17 we emphasized the algebraic definitions and properties of complex functions. In order to give a geometric interpretation of a complex function w = f(z), we place a z-plane and a w-plane side by side and imagine that a point z = x + iy in the domain of the definition of f has mapped (or transformed) to the point w = f(z) in the second plane. Thus the complex function w = f(z) = u(x, y) + iv(x, y) may be considered as the planar transformation

and w = f(z) is called the image of z under f.

FIGURE 20.1.1 indicates the images of a finite number of complex numbers in the region R. ...

Get Advanced Engineering Mathematics, 7th Edition now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.