History of Complex Numbers
Date: 12/12/2005 at 22:01:49 From: Audrey Subject: Why, and when were imaginary numbers created and by whom? I'm doing a project on imaginary numbers and I was stuck with the why. If you could explain without getting to in depth about hypercomplex numbers etc., (I'm a sophomore) that would be great!
Date: 12/12/2005 at 23:15:07 From: Doctor Peterson Subject: Re: Why, and when were imaginary numbers created and by whom? Hi, Audrey. Here is a good place to start; I found this by searching our site for the words "imaginary number history": History of Imaginary Numbers http://mathforum.org/library/drmath/view/52584.html The first link given in the answer has some more details. It mentions Cardan and Bombelli (in the 1500's), who were the first to work with complex numbers. What happened was that, in solving quadratic equations, it had previously been found that some equations could only be solved if you could take the square root of a negative number, which had been recognized to be impossible. But then when these people tried solving cubic equations, they found that for some equations, if they went ahead and did their work as if you COULD take the square root of a negative number, those "imaginary" numbers would eventually cancel one another out and you would be left with a real solution that WORKED. In other words, they made a trip through a world of numbers that presumably didn't exist, and came out at a proper destination in the real world, just as if those numbers they had used really meant something. In fact, they couldn't get to those solutions WITHOUT using imaginary numbers! That gave them the beginning of a sense that imaginary numbers were worth thinking about. So, over a long period of time, the rules for working with them, and appropriate notations, were developed, even though they were thought of as a sort of fiction that didn't feel quite valid. Eventually more was discovered about them that made them seem more and more "real", until they were finally accepted as being no less "real" than the real numbers. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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