Contents

## The basic concept of plural numbers

#### 1.Plural form

Remember“.** a+bi**（ a,b The number of the real numbers is called the plural.

#### 2.Imaginary unit

A similar unit can be pushed to PI, in which we use pi to represent PI, where Pi is 3.1415926…

Alike,** a+bi** The I in it represents a unit of imaginary numbers.“.

#### 3.The concept of the real part and the imaginary part

stay**a+bi**** **In this, we call it** a **It is the real part of the plural.

**b**** **It is the imaginary part of the plural.

#### 4.The distinction between pure imaginary numbers, plural numbers, and real numbers

We take shape as a form* bi *The number of numbers became

*Such as: 5I, 0.8i, 0.3i.*

**Pure imaginary number.**Then the plural is mentioned above, and then the Wayne diagram on the three is like this:

The basic concept of plural numbers is like the previous book.

## A reference to a complex number in geometry

#### 1.Complex plane

Two coordinate axes are introduced in the plane.

The abscissa unit is a real number, representing the real part of the complex number.

Then the unit of the longitudinal axis is a plural unit**i .**

#### 2.The relationship between the complex and the vector

In the coordinate system of the complex plane, the complex number* a+bi* Can be expressed as a vector

**(a,b)**For example, a vector in a graph coordinate axis is a complex number*a+bi.*

3.Conjugate complex number

Conjugate plural: for the complex number* z=a+bi*，For another plural

**z′=a-bi**，We call it

*For*

**z′***The conjugate complex numberz⎯⎯ 。*

**z**It is easy to find that a plural is equivalent to the real part of the conjugate complex, and the imaginary part is opposite.

After introducing the relationship between complex numbers and vectors, we can better understand the concept of conjugate complex numbers and explain them by vectors.**The conjugate complex is two vectors of the same size and about X axis symmetry.**

**4.The amplitude of the complex number**

**We can take the plural.z Writez=r×(cosθ+isinθ)，Among themr Pluralz Model lengthθ Pluralz The angle of the radiant.**

The amplitude of complex numbers**θ** In ordinary plane rectangular coordinates, the inclination angles of straight lines are quite similar.

A complex number has multiple radiant angles, and these values differ.2π.

Among them, we will

### θ∈[−π,π) Itθ Called the radiant angle**Main value.**

* *

**Basic operations of complex numbers**

For the complex number (a, b) and (C, d).Satisfy the addition rule (a, b) + (C, d)=(a±c,c±d). Satisfy the rule of multiplication (a, b) x (C, d)=(ac−bd,bc+ad) .

For division, the numerator denominator must be multiplied by the conjugate complex number of denominator, and the denominator will be real.

** The geometric meaning of complex multiplication is the multiplication of modular length and the addition of angles.**

——From NaVi_Awson

## Unit root of complex number

On the unit root of the complex number

**nSubunit root**.

**n Sub square**The unit circle will be divided into

**n Equal.**

**.n**The point is connected to a positive n edge.

**n**The starting point of the point is: (1,0)

**Root source**

**z^n=1**A root Z1, we think it is a root source.

**n Sub square**The result of the operation is 1.