Complex Numbers

Chapter 1 Introduction

The idea of ​​complex numbers dates back to antiquity. The beginnings are Heron and his considerations on the area of ​​a triangle. Then in the 16th … 17th century, people wondered “What if …?”. If there was such a number i whose product i*i=-1. It’s heresy! There can be a lot of “what if…?” in life. What if you harness the horse to the cart backwards? The only question is whether it will give us any advantage. Maybe it’s easier to back up the car? Maybe. But not very convincing. Therefore, the idea of ​​a reverse horse did not spread among carters.
It is different with complex numbers. Although their beginning is also “what if …?” however, it was the absurd assumption “i*i=-1” that solved the 3rd degree equation! And not only. Electricians liked them even more in the 19th century with the advent of alternating currents, which are sinusoids.
Note:
The number i with the assumption “i*i=-1” is the so-called imaginary number from the word imaginary. Mathematicians use it. On the other hand, for electricians it is j, unless it bites with the current i. I will continue to use the symbol j.