In mathematics, a number with a negative square is defined as a pure imaginary number. All imaginary numbers are complex numbers. This number has a special symbol "I" (imaginary number), which is called imaginary unit. It is defined as I 2 =-1. But the imaginary number has no arithmetic root, so √(- 1)= 1

But in electronics and other industries, because I is usually used to represent current, the imaginary unit is represented by J.

Imaginary number has no sign. They are not complex numbers of real numbers. Even pure imaginary numbers can't compare with size. 1 < 2 is right, but 1+I < 2+I is wrong.

We can draw an imaginary system in a plane rectangular coordinate system. If the horizontal axis represents all real numbers, then the vertical axis can represent imaginary numbers. Every point on the whole plane corresponds to a complex number, which is called a complex plane. The horizontal and vertical axes are also called real and imaginary axes.

The word "imaginary number" was invented by Descartes, a famous mathematician and philosopher in17th century, because the concept at that time thought it was a non-existent real number. Later, it was found that the imaginary number can correspond to the vertical axis on the plane, and it is as real as the real number on the horizontal axis on the corresponding plane. [Edit this paragraph] I will continue to make the following cycle for the property with higher power:

I1= me

i^2 = - 1

I^3 =-me

i^4 = 1

I^5 = me

i^6 = - 1 ...

Because of the special operation rules of imaginary numbers, the symbol I appeared.

When ω=(- 1+√3i)/2 or ω=(- 1-√3i)/2:

ω^2 + ω + 1 = 0

ω^3 = 1