You are familiar with the elementary functions of a real variable *x*. e^{x}, ln *x*, sin*x*, sin^{‒ 1}*x*, sinh *x*, sinh^{‒ 1}*x* 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.

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

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