# 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**.