Introduction to Complex analysis
complex analaysis is a branch of mathematics that deals with complex numbers, their functions, and their calculus. In simple terms, complex analysis is an extension of the calculus of real numbers to the complex domain. We will extend the notions of continuity, derivatives, and integrals, familiar from calculus to the case of complex functions of a complex variable. In doing so we will come across analytic functions, which form the centerpiece of this introduction. In fact, to a large extent complex analysis is the study of analytic functions. The basic ingredient of complex analysis is an analytic function, or that we know so well in calculus as a differentiable function. Any complex number z can be thought of as a point in a plane ( x,y ), so z = x+iy, where i=√-1. In a similar fashion, any complex function of a complex variable z can be separated into two functions, as in, f(z)=u(z)+iv(z), or, f(x,y...