# What is the absolute value of imaginary numbers, why not supernatural numbers?

• bananan
In summary, the conversation discusses the concept of absolute value for imaginary numbers and the possibility of creating "queer" numbers with different properties. It is explained that absolute value measures the distance from a number to 0, and therefore cannot be negative. The conversation also touches on the idea of exploring new mathematical concepts and their potential applications.
bananan
what is the absolute value of imaginary numbers, why not "queer" numbers?

the square root of -1 is "i".

the absolute value of an interger is itself, and of a negative number, it is a positive interger.

|-5| = 5
|5| = 5

what is
|5i| = ?
|-5i| = ?

why not invent a queer number?

the absolute value of a queer number is a negative number of the same interger value?

hence
|-5| = 5
|5| = 5
|5q| = -5
|-5q|= -5

Last edited:
The better question is why would one do this?

why does i need to invent absolute value? it is because it forms a norm. norm of an element gives a measurement such that we can compare mathematcal objects.

The better question is why would one do this?

same reason mathematicians asked "why Euclid's fifth postulate?"

maybe whole new mathematics may be invented/discovered. maybe it might unify physics.

Somehow I duobt it.

The point of an absolute value is that it determines the distance from 0 (absolutely... whatever that means). So if you're on the real line, a positive number is its size from 0, and a negative number is the negative of itself from 0. On the complex plane, you just use pythagoras on the line you draw with coordinates (x,y). If you can describe a system with negative distance, then fine, it has a negative absolute value (good luck with that).

By the way, you say why doesn't someone invent a number with the properties described above; you just did. Look how much good it did us ;)

Why don't you try playing around with the different properties that emerge from such a number and see if you find anything interesting (I already have actually)

bananan said:
same reason mathematicians asked "why Euclid's fifth postulate?"

maybe whole new mathematics may be invented/discovered. maybe it might unify physics.
I take it, then, that you don't know why mathematicians asked that! They had very good, cogent, reasons for wondering about the fifth postulate. There would be no point in "defining numbers whose absolute value is negative" because the whole point of absolute value is that it measures the distance from the number to 0 and distance is always positive.
We DEFINE absolute value to be positive because we want it that way! That was not the case for x2.

You could, of course, define a function f(x) by "f(x)= x if x is negative, -x if x is positive" which would give exactly what you say for number we already have. Of course, it wouldn't be "absolute value", if fact, it would be -|x|.

Office_Shredder said:
Why don't you try playing around with the different properties that emerge from such a number and see if you find anything interesting (I already have actually)

I'm interested in what you found, actually

Did you notice that this thread was over 4 years old?

Do people go "prospecting" in the archives?

bananan said:
why not invent a queer number?

the absolute value of a queer number is a negative number of the same interger value?

hence
|-5| = 5
|5| = 5
|5q| = -5
|-5q|= -5
Hey, I had an idea exactly like that!

HallsofIvy said:
Did you notice that this thread was over 4 years old?
Somebody came up with this idea 4 years before I did?

HallsofIvy said:
Do people go "prospecting" in the archives?
Occasionally.

I'll say that I am very interested in what will result from the queer number.

bananan said:
what is
|5i| = ?
|-5i| = ?
I believe that the answer to both is 5, am I correct?

For some complex number C in the form $$x+y\mathrm{i}$$, $$|C| = \sqrt{\Re(C)^2+\Im(C)^2}=\sqrt{x^2+y^2}$$.

So, for plus or minus 5i, this evaluates to 5.

HallsofIvy said:
Did you notice that this thread was over 4 years old?

Do people go "prospecting" in the archives?

I guess so! There was another "seemingly active thread" about closed form expressions that caught my eye today, as did the fact that some first-poster had resurrected it after years of inactivity...

The Chaz said:
I guess so! There was another "seemingly active thread" about closed form expressions that caught my eye today, as did the fact that some first-poster had resurrected it after years of inactivity...

The beauty of math is that it neither lives nor dies, but suffuses all of reality itself. Euler's identity was certainly true long before it was ever discovered.

That is the beauty of math?? I wish someone had told me earlier...

## 1. What is the absolute value of imaginary numbers?

The absolute value of an imaginary number is the distance between the number and the origin on a complex number plane. It is always a positive real number and is calculated by taking the square root of the sum of the squares of the real and imaginary parts of the number.

## 2. How is the absolute value of imaginary numbers different from real numbers?

The absolute value of imaginary numbers is different from real numbers because imaginary numbers involve a square root of -1, which makes them non-real numbers. Real numbers, on the other hand, do not involve any square roots of negative numbers.

## 3. Why are imaginary numbers represented by the letter "i"?

The letter "i" is used to represent imaginary numbers because it stands for "imaginary". This notation was first introduced by mathematician Leonhard Euler in the 18th century and has since become the standard notation for imaginary numbers.

## 4. Can the absolute value of imaginary numbers be negative?

No, the absolute value of imaginary numbers can never be negative. As mentioned earlier, it is always a positive real number. However, the imaginary part of an imaginary number can be negative.

## 5. Why are imaginary numbers considered to be "imaginary"?

Imaginary numbers are considered to be "imaginary" because they involve the square root of -1, which does not have a real solution. They are a concept in mathematics that helps to solve certain problems and cannot be directly measured or observed in the physical world.

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