In this paper we discuss the implications of the complex and its rotation. The complex is very interesting, this article introduces the basic definitions and properties of the complex, and its geometric significance of rotation.
The complex is extremely important for both rotation:
1. It introduces a rotation operator (rotational operator) ideas: can represent a complex rotation transformation.
2. It is the quaternion and multi-vector intrinsic properties.
While we do not discuss quaternion and multi-vector (later article will explain), but we will discuss the rotation plural meaning ( the complex plane 2D rotation on), as well as the introduction of the rotator (the Rotor) , we found that a specific complex 2D can be described as a rotation.
Introduction
Complex (complex number) , also known as the digital realm of the "King", which can solve the problems of ordinary real numbers are not well resolved.
For example, for the following equation:
$$x^2+1=0$$
Despite such a simple equation, but there is no real solution. In fact, the real number can not solve this problem:
$$x=\sqrt{-1}$$
But this did not prevent mathematicians find a way to solve such problems, they make a very cattle very simple idea is to recognize the existence of $ i $, which meet the $ i ^ 2 = -1 $, so the previous equation we can solve:
$$x=\pm i$$
Then $ i $ in the end what is it? We do not have to tangle, $ i $ is a mathematical tool mathematician proposed a simple mathematical object, to meet the $ i ^ 2 = -1 $. This article will explore how this mathematical tool to rotate to play a role.
to be continued. . .
Plural base
The definition of complex numbers
Plural nature: axiom
Plural mold
Complex addition and subtraction
Complex scalar multiplication
The product of two complex numbers
Conjugate complex
Two complex division
Inverse complex
Complex and rotation
Complex plane
Polar coordinates
Rotator