ABSTRACT
The theory of functions of a complex variable is a basic part of mathematical analysis. It provides some of the very useful mathematical tools for science. A complex number, containing two real numbers, can be represented by a point in a two-dimensional plane, known as the z-plane, or complex plane, or Gauss plane. Complex polynomials are continuous everywhere. Quotients of polynomials are continuous whenever the denominator does not vanish. For complex functions, rules for differentiating sums, products and quotients are, in general, the same as for real-valued functions. The exponential function is of fundamental importance and also as a basis for defining the other elementary functions. Any function that has continuous partial derivatives of second order and that satisfies the Laplace equation is called harmonic function.
