Linked Questions

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 ?
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: $$...
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 ...
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 $x$...
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....
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 ...
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
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. ...
0
votes
2answers
56 views

If ‘i’was invented to take the square roots of negatives, why can’t we invent a concept to divide by zero? [duplicate]

As explained in the title, if i is used to simplify expressions involving the square root of a negative number, is there another concept which allows us to simplify expressions involving zero on the ...
-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 ...
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 ...

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