In the movie Proof (2005) Hal Dobbes is a mathematician graduate whose rock and roll band “plays” a song called ‘i’. Get the joke? When the band “plays” the song, they are not really “playing” anything because the song is “imaginary”. Have you ever wondered what exactly ‘i’ is?
Whenever you see the symbol ´i´, probably the first thing you think is that it’s just an italicized ‘i’, a normal letter in the alphabet. Or maybe you don’t even think about it at all. Although, it’s right that it is in fact just an italicized `i´, there is a mathematical definition that goes a step further than that. The symbol ‘i’ stands for imaginary numbers.
To define an imaginary number, you must grasp the concept of what a real number is. A real number is any number that exists in a timeline. Examples of real numbers are : ½, -20.5, 3, 0, etc. Now that you know real numbers, we can discuss what is ´i´. According to math, this symbol simply means the square root of -1. This might sound a little strange because up until now you might have been taught that it’s impossible to take square roots of negative numbers. But guess what? It is possible. It’s just that nobody believed in a “real world” use for this new number at first other than calculating certain equations. Everybody knew it wasn’t ‘real’, and this was getting pretty complex.
Well, as people were forced to use the ‘i’, they eventually realized that the ‘i’ was used in equations along with other real numbers. This was confusing, so people used the term “complex numbers” to refer to real numbers plus imaginary numbers. For example, 2 ⍏ 3i.
Today, the ‘i’ is considered one of the most important numbers. Complex numbers have helped us study the physical phenomena in many different ways such as in quadratic formulas to figure out how electrical circuits or forced spring systems work, how the movement of shock absorbers of a car work over a bump, modeling fluids of various objects, and more.
This is all thanks to the Greek mathematician and engineer Heron of Alexandria and Rafael Bombelli who further developed the rules and usage of complex numbers. Then there is René Descartes who actually gave them the name “imaginary” numbers in his book “La Geometrie”. “For any equation one can imagine as many roots, but in many cases no quantity exists which corresponds to what one imagines.”- Descartes.
Imaginary numbers aren’t just for us to overlook as we always do like Augustin Louis Cauchy stated “We completely repudiate the symbol √ −1, abandoning it without regret because we do not know what this alleged symbolism signifies nor what meaning to give to it.” Just know that imaginary numbers exist because they are important and have a real world use; stop daydreaming and pay attention to them in math class. 😉
This article cites:
<http://mathforum.org/dr.math/faq/faq.imag.num.html>.
<http://www.math.uri.edu/~merino/spring06/mth562/ShortHistoryComplexNumbers2006.pdf>.
<http://mathforum.org/library/drmath/view/53844.html>.
<http://www.innovateus.net/science/what-imaginary-number>.
<http://mathworld.wolfram.com/i.html>.
