Where Did i Come From?

When I was in school and I learned about imaginary numbers, I honestly thought it had been dreamed up by a bunch of drunk mathematicians who didn’t have anything better to do. Yes, I know that’s wrong but when you are 16, you think you know it all. Since then, I’ve learned more about I and my story is just that a story.

Let’s rewind history back to the 1500’s in Venice where all the formulas used to solve equations were guarded closely, much like companies guard proprietary recipes. One man, Niccolo Tartaglia, had a real interest in quadratic and cubic functions due to working with ballistics and fortifications. Niccolo and others realized that many of the quadratic and cubic functions had solutions needing the square root of a negative number.

Niccolo and a competitor discovered if they used negative square roots, they would still get proper numerical answers. Thus mathematicians began using I to represent the square root of -1. The one problem with this definition is that it went against the knowledge that a negative times a negative produce a positive number. When you square I you get I^2 = -1 and it took people a long time to be comfortable with that idea. 

Another reason, it took people so long to accept this whole idea had something to do with the fact that the square root of -1 could not be shown via a graph or using geometry.  Mathematician Rafael Bombelli wrote a titled Algebra in 1572 in which he tried to explain math to people who had not studied it. In the book he declared that imaginary numbers were neither positive nor negative and did not follow the normal rules because he got around it by stating it as sqrt(-1) rather than i.  

Descartes called them imaginary numbers because they were imagined solutions.  This lead to other mathematicians accepting the term and eventually they came up with the Fundamental Theorem of Algebra which states that the number of solutions of an equation are equal to the highest degree. This theorem was not proven until 1806 by Jean-Robert Argand who worked on relating imaginary numbers to geometry through the use of complex numbers.  

About the same time, Frederich Gauss declared that imaginary numbers were not made up and could actually be visualized because they made perfect sense.  Once should look at the idea these are not real numbers but exist as an extension to the real number line while Euler came up with the accepted letter we now use.

For the most part, imaginary numbers remained in the range of the theoretical until recently when modern electronic age. Imaginary numbers are used when analyzing any kind of waves from electromagnetic radiation (wi-fi, radios) to audio signals (music, AC).

So now you have a short history of the imaginary numbers.  Let me know what you think, I'd love to hear.  Have a great day.