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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 distinguish analytic functions from generic complex-valued functions of complex variable, we use the notation f(x) for the former and …
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 + i sin a)^n = cos na + i sin na, where n is natural numbers. …
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, and the imaginary part by a displacement along the y-axis. The Complex Plane Cartesian Plane …
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 need to identify x and y. Modulus is represented with |z| or mod z. In this …
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 of complex numbers. The real part of complex numbers is represented in the x-axis and Imaginary part …
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 (a-c)-i(b-d) i.e (a-ib)-(c-id) = (a-c)-i(b-d) Example: 2. …
Operation of Complex Numbers on Division and Substraction Read More »
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. Each has two terms, so when we multiply them, we’ll get four terms: (3 + …
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 get as follows; (a + ib) + (c + id) = (a + c) + …
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 diagram or complex plane by drawing the point x + iy ∈C as the point …
Gentle Introduction and Basics of Complex Analysis Read More »