### 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**.