imaginary number

Why did mathematicians feel the need to have an imaginary number denoted i and (i^2=-1). How is an imagianry number applicable to real life? How do mathematics prove an imaginary number, I mean how did they determine that i^2 is equal to -1?

Peace

Hawking talks about imaginary numbers in “breif history of time”, I remember him saying that imaginary numbers may be more real then real numbers. Now my memory is dicy concerning imaginary numbers… but I think… I think (could be wrong) I’ll look it up in my copy sometime tonight, and get back to you, but I think that negative numbers are a way of dealing with negative energy.

At any rate it really isn’t any more imaginary then any other type of numbers. When Neuton came up with his theory of gravity he realized the math wasn’t invented yet to explain the theory. He was such a genius that he made the math, and hence we now have calculus. Imaginary numbers are the same thing, we came upon yet another area where the math wasn’t invented yet, and so they invented imaginary numbers… and I think its to deal with negative energy, or anti-matter.

Newton was insane you know he stuck a needle in his eye to see what would happen?

I wouldnt call him insane. Actually you probably owe your eyes to him. Because of newton, we now know not to stick needles in our eyes :slight_smile:

Hi curious_rina

In order to prove the fundamental theorem of algebra Gauss needed to include roots of negative numbers. By setting i=-1^½ he was able to get this solution.

The first person to use this construct was Girolamo Cardano who was working on the solutions to the cubic and quartic equations in 1539.

One of the most useful functions in physics is the Fourier transform which makes use of i.

Imaginary numbers are very important in the field of electrical engineering. If you have a parallel RC circuit and apply a voltage to it, the current flowing through the resistor will be ‘real’ and the current flowing through the capacitor will be ‘imaginary’. Therefore, the impedence will equal: X = R - iC. Its basically a way to describe (in the EE perspective) the current lagging the voltage by 90 degrees.

In cartesian co-ordinates, the y-axis is considered the imaginary axis and the x-axis the real. Any imaginary current flowing through the capacitor will be on the y-axis and any real current flowing through the resistor will be on the x-axis. The total current flowing will be the resultant between both currents.

Thanks for the info. I was curious about it because my professor just started her lectures and never really explained what is really was. I guess she assumed everyone was familiar with it because all I knew was that we ended up solving systems of equations with this imaginary number. I guess I feel satisfied with the idea and usefulness of imaginary numbers now. It’s like hiding the problem to get an answer… hmmm …we can’t find the root of a negative number, so mask it with an i instead and solve… would this be considered an exception to an existing rule, or just a new rule.

Peace

What your professor probably demonstrated is that the solutions you get are real-number solutions and that they can be 100% verified to be actual solutions to the equation (usually by substituting them back in).
So don’t think that there’s some kinda magic justification there to accept those solutions as solutions. Once you have 'm, they are solutions whether you consider imaginary numbers or not. (it can be verified that they are without a mention of imaginary numbers)

I once entertained this question myself. I am a math major and found out that Imaginy numbers have uses in so many facets of society. For instance, imaginary electriity is used by flourescet ligth bulbs. I don’t exactly understand the idea, but “J” (equivelent to i in math) is very used in electrical enginering. I dunno if this helps, but…it is very useful.

–There is No Truth