The square root of minus 1

Post Reply New Topic

There is a branch of mathematics that requires the use of imaginary numbers namely;

The square root of -1, (otherwise known as 'i' or 'j', when I studied it)

Any number squared, including negative numbers, results in a positive number, so -1 has no real number square root.

Of course, as soon as 'i' is squared, it becomes -1 and moves back into real number mathematics.

How are you with the imaginary number concept?

I didn't understand this very well when I learnt it. I don't understand the point of imaginary numbers.

Its not hard for me. All you had to know is i=sqrt(-1) and build on the concepts from there.

I understand it, but I do not believe it is founded in reality. It's a useful trick, that's all.

Taken from somewhere else:

For example, in electrical engineering, when analyzing AC circuitry, the values for the electrical voltage (and current) are expressed as imaginary or complex numbers known as phasors. These are real voltages that can cause damage/harm to either humans or equipment even if their values contain no "real part". The study of AC (alternating current) entails introduction to electricity governed by trigonometric (i.e. oscillating) functions. From calculus, one knows that differentiating or integrating either "+/- sin(t)" or "+/- cos(t)" four times (with respect to "t," of course) results in the original function "+/- sin(t)" or "+/- cos(t)." From complex algebra, one knows that multiplying the imaginary unit quantity "i" by itself four times will result in the number 1 (identity). Thus, calculus can be represented by the algebraic properties of the imaginary unit quantity (this was exploited by Charles Proteus Steinmetz).

Error 2

It's sort of like infinity.....I can grasp it as much as it's able to be grasped, and sometimes drive myself crazy trying to understand it further.LOL

Differential equations are used to model process that behave differently depending on the properties of the complex root of the equation. The only thing I learnt at college about imaginary numbers!

It is a weird idea, and I wouldn't say I understand it deeply (I can do math, but I could never be a mathematician), but it sure is useful.

I.e. expressing sine&cosine in terms of e^(i x) -- makes the math of anything involving waves so much easier (quantum mechanics, optics, electromagnetism, etc etc)

Thanks for this.

Yes, that's what I always liked about it.

It is necessary to invent something in order for a branch of mathematics to actually exist.

hmmmm, i remember having learned something like that in high school.

It's interesting, although i forget what it was useful for exactly

I think it was useful for the quantum physics course I took but then again, I failed that course and didn't know what was going on.

It took me quite a while to grasp the concept back in 10th grade, but eventually I did.

But I still hated i

what about i^3? do you just have -i?

I barely passed Algebra 1 & that's the highest math I took. Are the imaginary numbers the letters in math problems that you have to find a number for

No. Thats not what the term means.

Not a mathematician but I do know that the letters in the algebra equations are called "variables". They stand for whatever kinda numbers are involved in the problem at a hand (which are usually regular old real numbers). Though they could stand for imaginary numbers as well.

Imagine the regular real numbers lined up single file. The positive numbers going to the right from zero (1,2,3,..), and the negative numbers going to left from zero. The "imaginary" numbers are like a second ghost family of numbers going on an axis straight up perpendicular to the line of real numbers (also starting at the zero point) going "square root of negative one", "square root of negative two", and so on. In lower math your taught that negative numbers dont have square roots (if you square either a postive or negative number you get a postive number), and I for one cannot imagine HOW a negative number could HAVE a square root. But in more advanced math they change their minds and teach you that negative numbers actually have do square roots and that these square roots are what are called "imaginary numbers".

A high school teacher, and a book I read as a kid, both mentioned the concept (the book even said that "imaginary numbers are perfectly real"), but what I said above is as far as I got with it.

Imaginary numbers seem to be just that to me (rather imaginary). But a poster above says that imaginary numbers are actually of practical use in electrical engineering, and even explains how. I will have to take his word for it- his explanation is beyond my math ken. Lol!