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

[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

 

[DeadWolfe]

The better question is why would one do this?

 

[leon1127]

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.

 

[bananan]

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.

 

[DeadWolfe]

Somehow I duobt it.

 

[Office_Shredder]

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)

 

[HallsofIvy]

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|.

 

[R1ckr()11]

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

 

[HallsofIvy]

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

Do people go "prospecting" in the archives?

 

[FtlIsAwesome]

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!

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

Somebody came up with this idea 4 years before I did?

Do people go "prospecting" in the archives?

Occasionally.





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

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

I believe that the answer to both is 5, am I correct?

 

[jhae2.718]

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.

 

[The Chaz]

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...

 

[R1ckr()11]

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.

 

[The Chaz]

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