# Category: complex analysis

Learn Complex Analysis, Higher Mathematics at Hack Smile. hacksmile.com

### Function of a Complex Variables

A complex function of a function of a complex variables is a function whose domain and range are subsets of the complex plane. This is also expressed by saying that the independent variable and the dependent variable both are complex numbers. If f(x) is analytic everywhere in the complex plane, it is called entire function. To Read more…

### The De Moivre’s Theorem

The process of mathematical induction can be used to prove a very important theorem in mathematics known as De Moivre’s theorem. The De Moivre Theorem  formula useful for finding powers and roots of complex numbers. The De Moivre Theorem example (cos a Read more…

### The Complex plane

The complex plane (or Argand plane or Gauss plane) is defined as a way to represent complex numbers geometrically. Basically, it’s a modified Cartesian plane, with the real part of a complex number represented by a displacement along the x-axis, Read more…

### Modulus or Absolute value of Complex Numbers

Modulus is the length of a vector. The length is the distance between two points. To find the modulus of a complex numbers is similar with finding modulus of a vector. For a given complex number, z = 3-2i,you only Read more…

### The Complex Plane (Cartesian Plane)

Complex plane can be thought to be modified Cartesian plane, with the real part of a complex number represented by a distance along the x-axis, and the imaginary part by a displacement along the y-axis. The concept of the complex plane allows a geometric interpretation Read more…

### Operation of Complex Numbers on Division and Substraction

The operation of complex numbers on Subtraction is simple in a way  that one have to do the normal subtraction Example: 1. (a-ib)-(c-id) . In this example, one is required to separate between Real part and Imaginary part. By doing so you’ll have Read more…

### Complex Analysis: Operation on Multiplication

Complex multiplication is not difficult operation to understand from either an algebraic or a geometric point of view. We can do it algebraically first, and let’s take specific complex numbers to multiply, say 3 + 2i and 1 + 4i. Read more…

### Operation on Complex Analysis ~ Addition

We simply add the complex number of the form (a+ib)+(c+id) and get the two parts of Complex number i.e Real part, Re{z} and Imaginary part, Im{z}. If a + ib, c + id ∈ C then we can add and Read more…

### Gentle Introduction and Basics of Complex Analysis

A complex number is an expression of the form x + iy where x, y∈R We denote the set of complex numbers by C (Here i denotes √−1 so that i^2 = −1.). We can represent C as the Argand Read more…