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Complex Analysis by ITL ESL

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3

Elementary Functions

3.1 INTRODUCTION

You are familiar with the elementary functions of a real variable x. ex, ln x, sinx, sin‒ 1x, sinh x, sinh‒ 1x are some of the examples of elementary functions of x. In this chapter, we will define the corresponding elementary functions of a complex variable z = x + iy that reduces to elementary functions of real variable x when y = 0. We will first discuss about the exponential function of a complex variable and use this function to develop trigonometric, hyperbolic and logarithmic functions. Further, with the help of multivalued functions, we will explain the branches of logarithmic functions.

3.2 ELEMENTARY FUNCTIONS

An algebraic function of a complex variable z is a polynomial, a rational function ...

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