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### 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?
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 ...
60 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" ...
650 views

### Why non-real means only the square root of negative?

Once in 1150 AD, an Indian mathematician Bhaskara wrote in his work Bijaganita (algebra) that, There is no square root of a negative quantity, for it is not a square However later on in 1545 an ...
92 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. ...
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: ...
757 views

### difficulty of accepting $i^2 = -1$ for first timers [duplicate]

While teaching complex numbers for those who are encounter for the first time (usually 10th grader and 11th grader), I get the question like "Can even squared number give negative results? How ...