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# Functions of Complex Variable

DOI link for Functions of Complex Variable

Functions of Complex Variable book

# Functions of Complex Variable

DOI link for Functions of Complex Variable

Functions of Complex Variable book

## ABSTRACT

The set of complex numbers is an extension of the set of real numbers. An expression of the form z = x + iy, where x and y are real numbers, is called a complex number, and the symbol i is called the imaginary unit: i2 = –1. The numbers x and y are called, respectively, the real and imaginary parts of z and denoted by

x = Re z and y = Im z. (10.1.1.1) The complex number x + i0 is identified with real number x, and the number 0 + iy is denoted by iy and is said to be pure imaginary. Two complex numbers z1 = x1 + iy1 and z2 = x2 + iy2 are assumed to be equal if x1 = x2 and y1 = y2.