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Complex Analysis by ITL ESL

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8

Bilinear and Conformal Transformations

8.1 INTRODUCTION

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 LINEAR TRANSFORMATIONS

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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