Where did the square root of negitive 1 come from?

Question

I know it's represented as "i" and that it's imaginary. I'd like to know where the idea came from.

Answer 1

Wikipedia: http://en.wikipedia.org/wiki/Imaginary_numbers

Answer 2

The square root of -1 comes up in the solution of 3rd degree algebraic equations. There is a "cubic formula" which is the analogue of the "quadratic formula" for which real solutions nevertheless require the use of "imaginary numbers" in an intermediate step.

This was the first big hint that imaginary numbers have some place in the system of mathematics. For a long time--even today by nonmathematicians--they were seen as "extra" and somehow not legitimate, but this was the case with negative numbers for a long time, too. As for negative numbers, the key to their acceptance is the geometric interpretation of where they come from. In this case, it's the "complex number plane" which is a generalization of the "real number line."

Answer 3

In George Lakoff's and Rafael Nuñez "Where Mathematics Comes From?" :

"Suppose you ask,"Find a number that, when multiplied by itself and aded to one, gives you zero. Or, equivalently, solve the equation x^2 +1= 0. This is a very simple equation, with numbers 1 and zero and the operations of multiplication and addition ...

"Subtracting one from both sides of the equation, we get x^2 = -1. If x is a number as closure requires, it has to be either a natural number, an integer, a rational a real, or some other kind of "number." Let us call this number "i" for short, i has the basic properthy that i^2=1.

"Is i a real number? That is, is ti ordered relative to al numbers we call 'real?' "

I recommend you get the book and follow their argument. I'll add that they do haave a very interesting couple of pages on "The Conceptualization of Negative Numbers" as well.

Answer 4

The idea came from the fact that certain equations, such as X^2 + 1 = 0 have no solution using just the real numbers.

Complex numbers are an extension of the real numbers to allow you to solve those equations.

Answer 5

Get a book on complex analysis, not Lakoff's book. It has many mistakes in it, and it will give you faulty intuition if you internalize it. Lakoff is not a mathematician.

By the way, there is no *the* squart root of -1. i is defined so that i^2 = -1, but you cannot simply take the square root of both sides of that because sqrt(-1) is not unique. i is *a* square root of -1, but it is not *the* square root of -1.

Answer 6

this came when some one wanted to sovle quadratic equation like x^2+1 = 0

Answer 7

i think that "i" came about when mathmaticians wanted to work with imaginary numbers, and just thought that "i" would be an easier way to note and factor them
"i" notation really does help, in my opinion

Answer 8

it is used in an electrician's profession