Imaginary part: For the complex number z=x+iy, the equation is satisfied, where x and y are arbitrary real numbers, x is called the real part of the complex number z, and y is called the imaginary part of the complex number z ... Complex number is a domain extension of ordinary real numbers, aiming at solving problems that cannot be solved simply by real numbers.

Imaginary number: In mathematics, even numbers whose exponential power is negative are defined as pure imaginary numbers. All imaginary numbers are complex numbers. Defined as me? =- 1。 But the imaginary number has no arithmetic root, so √ (-1) = i. For z=a+bi, it can also be expressed in the form of iA power of e, where e is constant, I is imaginary unit, and A is imaginary amplitude, which can be expressed as z=cosA+isinA.

A pair of numbers consisting of real numbers and imaginary numbers is regarded as a number within the range of complex numbers, so it is called a complex number. Imaginary number is neither positive nor negative. Complex numbers that are not real numbers, even pure imaginary numbers, cannot compare sizes.

2. Different origins

Imaginary part: The concept of complex number originated from the Italian mathematician gerolamo cardano in16th century. When he tried to find the general solution of cubic equation, he defined I as "fiction"

Imaginary number: the word imaginary number was founded by Descartes, a famous mathematician in the17th century, because the concept at that time thought it was a non-existent real number. Later, it was found that the real part A of the imaginary number a+b*i can correspond to the horizontal axis and the imaginary part B can correspond to the vertical axis on the plane, so that the imaginary number a+b*i can correspond to the points (a, b) on the plane.

3. Different expressions

Imaginary part: in English, Real numbers aRe real quantities, so the first two letters "re" of real are generally taken to represent the real part of complex numbers; The Imaginary number is an imaginary number, so the first two letters "im" of the imaginary number are generally taken to represent the imaginary part of the complex number. For example:

Re(2+3i)=2，Im(2+3i)= 3；

Re(-7.38i)=0，Im(-7.38 I)= 7.38。

Complex plane representation

The point (x, y) on the complex plane represents the complex number x+iy, where the y axis is the imaginary axis and the value of y is the imaginary part.

Imaginary number: a=a+i represents a concept that has nothing to do with everything. No matter what happens to A, I won't change.

References:

Baidu Encyclopedia-Xubu

References:

Baidu encyclopedia-imaginary number