Why do they exist? We don't talk to imaginary people, we don't have imaginary pets, or eat imaginary food...so why do we calculate imaginary numbers...and if there is a reason...who came up with the brilliant idea to name them "imaginary"!
2007-02-06 17:09:43 · 10 answers · asked by ♥ Yaz ♥ 2 in Science & Mathematics ➔ Mathematics
the imaginary unit, i, is defined as
i= sqrt(-1).
Obviously there is no real number that is the square root of an imaginary number. However, in doing math problems you inevitably need to take square roots of negative numbers, which you can't do. Thus, mathematicians created the imaginary, or complex, numbers in order to be able to solve these problems. They're called imaginary because they don't exist in any tangible form in the real world.
Remember, all of math is just stuff we humans have made up ourselves. There is no such thing as "2" in real life, it is just a concept we have created to describe certain amounts. All of math- numbers, matrices, vectors, statements, sets, etc. are all just concepts we have created to help us describe actual stuff in the real world. In the case of imaginary numbers, it doesn't describe any tangible object in the real world, but it makes our math work out.
2007-02-06 17:16:51 · answer #1 · answered by kz 4 · 0⤊ 0⤋
Yes, there is a reason. Mainly to be able to express the solutions of equations like x^2 + 1 = 0, which has no real solutions. Equations and formulas that lead to imaginary numbers come up frequently in the sciences and engineering. Voltage, current, and power, for example, are some of the quantities that can be expressed in terms of imaginary numbers.
2007-02-06 17:18:24 · answer #2 · answered by vaca loca 3 · 0⤊ 0⤋
If you're talking about i (which is the square of negative one), imaginary (the preferred term is complex) numbers exist because they have many applications in electronics; they are used for rotating vectors.
In essence though, ALL numbers are imaginary. Have you seen the number 2? I certainly haven't seen the number 2. I've seen the symbol 2, and I understand the concept of having 2 of something. But I haven't seen the number 2. For that reason, ALL numbers are imaginary anyway.
2007-02-06 17:16:53 · answer #3 · answered by Puggy 7 · 1⤊ 1⤋
The name arose because there is no real number which solves x^2 = -1. So, we define an imaginary unit, with the symbol i, which is by definition a solution of this equation. The concept turns out to be of vital importance to mathematics. As to who thought up the name, I don't know.
2007-02-06 17:15:00 · answer #4 · answered by Anonymous · 0⤊ 0⤋
It's just a placeholder in order to solve problems.
You will find out that there are many questions that have an even root of a negative number (which gives you an imaginary number), but you go further to find real numbers in some of these problems. You need the imaginary part to solve it.
2007-02-06 17:14:15 · answer #5 · answered by Anonymous · 1⤊ 0⤋
They aren't really called imaginary numbers anymore. That term was first used in the 1500's, when mathematicians thought that these numbers didn't exist.
However since then ideas have changed. Today they are usually called complex numbers, as they are made up of two parts, one more traditional part, and a complex part that contains the square-root of a negative number, such as a+bi, where i=(-1)^(1/2)
They are important today in area of study like signal processing, control theory, electromagnetism, quantum mechanics, and cartography.
2007-02-06 17:20:06 · answer #6 · answered by Penguin 2 · 2⤊ 0⤋
The known numbers were called the "real" numbers. When the mathematics for these addition numbers was developed, what were they going to call these addtional numbers that were "not real". The decision was to call them "imaginary".
However, imaginary numbers are used to solve real problems in the real world. Their label is perhaps unfortunate. They do after all, exist.
2007-02-06 17:22:06 · answer #7 · answered by Northstar 7 · 2⤊ 0⤋
negative numbers are less than zero. if zero means nothing, how can we have something less than zero....
we dont talk to negative people, we dont have negative pets or eat negative food.
but if you can live with that, I think you can live with imaginary numbers as well.
the point is, they are just abstractions, decimals, fractions, all of them. including zero.
they are not real, but have real uses !
2007-02-06 17:32:29 · answer #8 · answered by novice 4 · 2⤊ 0⤋
In addition to solving many mathematics problems, they're also important in some real life physics and engineering math problems. See:
http://www.math.utoronto.ca/mathnet/answers/relevance.html
2007-02-06 17:19:36 · answer #9 · answered by Bob 7 · 1⤊ 0⤋
they are basically just a tool for solving complex problems. they don't actually "exist"
2007-02-06 17:14:39 · answer #10 · answered by Critical Mass 4 · 0⤊ 2⤋