Bilinear and Conformal Transformations


In Chapter 2, we have defined the term transformation or mapping. We saw there that if corresponding to each point z = (x, y) in z-plane, we have a point w = (u, v) in w-plane, then the function w = f(z) defines a mapping of the z-plane into the w-plane. In this chapter, we will discuss how various curves and regions in the z-plane are mapped to those in the w-plane by elementary functions. Specifically, we develop the theory of bilinear transformation and explain the concept of conformal mapping with the help of some frequently used elementary functions.


8.2.1 Translation: w = z + b, where b is any Complex Constant

Writing z = x + iy, b = α + and w =

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