Linked Questions

5
votes
3answers
165 views

Why there is no value for $x$ if $|x| = -1$? [duplicate]

According to the definition of absolute value negative values are forbidden. But what if I tried to solve a equation and the final result came like this: $|x|=-1$ One can say there is no value for $x$...
5
votes
3answers
106 views

Why not define $|v| = -1$? [closed]

I was wondering why if we have $i^2 = -1$, why not have a "number" $v$ such that $|v| = -1$? Does anything interesting arise from considering this system? The only thing I could come up with was: $$...
4
votes
3answers
317 views

Why don't we define division by zero as an arbritrary constant such as $j$? [duplicate]

Why don't we define $\frac 10$ as $j$ , $\frac 20$ as $2j$ , and so on? I know that by following the rules of math this eventually leads to $1=2$ , but we could make an exception and say that $j$ is ...
2
votes
3answers
176 views

Analogous numbers to i

$i$ is defined as the square root of $-1$. I was wondering if number systems other than the complex numbers can be reached from the real numbers by a similar process. Like a number whose $\sin$ is $1....
9
votes
2answers
547 views

Could we invent a new number with $|p|=-1$?

We know that how a single definition $i^2=-1$ revolutionized our mathematics and solved many many problems. I wonder whether the definition $|p|=-1$ could have the potential of creating a new ...
3
votes
2answers
85 views

What type of division is possible in 1, 2, 4, and 8 but not the 3rd dimension?

In this article that talks about some history of hamilton http://plus.maths.org/content/curious-quaternions There is a snippet that says this: Multiplication is very sneaky. You can only set up ...
2
votes
2answers
151 views

Is there an impossible to solve equality in $\mathbb{C}$?

exactly like how ${x^2=-1}$ is impossible in $\mathbb{R}$ is there any equation that is impossible in $\mathbb{C}$ and how to deal with ?
1
vote
2answers
1k views

Could 1/0 be an imaginary number? [duplicate]

There is no way to find the square root of a negative number. It just doesn't work. So the answer to the impossible question, "What number squared equals a negative number?" is just said to be $i$, an ...
2
votes
1answer
67 views

If $i^2=-1$, at one point undefined, then why not define $\frac00$? [duplicate]

Would this even assist math in the way that $i$ did? Or is this just outright pointless and/or too exclusive to call for a definition?
2
votes
1answer
91 views

How come complex numbers encompass all the numbers we need?

Are there numbers other than complex numbers? for example, \begin{eqnarray} |x| = -1 \end{eqnarray} Surely, the equation does not make much sense initially since by definition magnitude is positive. ...
1
vote
1answer
81 views

Extending the complex numbers by the solution of $|x| = -1$

I don't think I've ever encountered a situation where I've wanted to solve equations of the form $|x| = -1$, but you often hear that mathematics should be explored for the sake of mathematics. I'm ...
0
votes
1answer
49 views

What kind of quantities are $\frac{2}{0}$ and $\sqrt{-2}$?

I came across this interesting problem in my book : What kind of quantities are $\frac{2}{0}$ and $\sqrt{-2}$? All I know is that $\frac{2}{0}$ is undefined while the second one is a complex ...
-1
votes
1answer
47 views

What distinguishes $i$ as an 'imaginary number' worth study versus other numerical ideas/numbers that should not/do not exist?

In an earlier post, I entertained the idea that a number (would it be a number? Well, it would be something) $Φ$ existed such that the interval $[0,Φ]$ would include only $0$ and $Φ$. In other ...
3
votes
0answers
870 views

Are complex numbers complete in every way?

I was told many times a story. Indeed a fascinating one to me as a student learning mathematics. First there were natural numbers. People started adding things and finding solutions to finding the ...
3
votes
0answers
59 views

Why is there only one type of imaginary number? [duplicate]

We've defined the square root of -1 as an imaginary number i (or j, if you're a physicist). Is there any reason why we can't/haven't made other systems of imaginary numbers for other "impossible" ...

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