On imaginary numbers to be learned in senior high school

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. Defined as I 2 =-1. But the imaginary number has no arithmetic root, so √ (-1) = i. For z=a+bi, it can also be expressed as the form of power iA of e, where e is constant, I is imaginary unit, and A is imaginary amplitude, which can be expressed as z=cosA+isinA.

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

Imaginary number is neither positive nor negative. Complex numbers that are not real numbers, even pure imaginary numbers, cannot compare sizes. 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 have also been renamed as 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, which is as real as the real number corresponding to the horizontal axis on the plane. [Edit this paragraph] My attribute, my high power, will continue to do the following cycle:

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