- The basic concept of plural numbers
- A reference to a complex number in geometry
- Basic operations of complex numbers
- Unit root of complex number
The basic concept of plural numbers
Remember“.a+bi（ a,b The number of the real numbers is called the plural.
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
staya+bi In this, we call ita 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 formbi The number of numbers becamePure imaginary number. Such as: 5I, 0.8i, 0.3i.
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
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 uniti .
2.The relationship between the complex and the vector
In the coordinate system of the complex plane, the complex numbera+bi Can be expressed as a vector(a,b)
For example, a vector in a graph coordinate axis is a complex numbera+bi.
3.Conjugate complex number
Conjugate plural: for the complex number z=a+bi，For another pluralz′=a-bi，We call it For The conjugate complex number 。
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 numbersθ 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
It Called the radiant angleMain 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.
Unit root of complex number
On the unit root of the complex number