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### 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 ...
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### What allows us to use imaginary numbers?

What axiom or definition says that mathematical operations like +, -, /, and * operate on imaginary numbers? In the beginning, when there were just reals, these operations were defined for them. Then,...
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### 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 ...
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### A new imaginary number? $x^c = -x$

Being young, I don't have much experience with imaginary numbers outside of the basic usages of $i$. As I was sitting in my high school math class doing logs, I had an idea of something that would ...
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### Is it possible to have a 3rd number system based on division by zero?

Is it possible in mathematics to use a third number line based on division by zero; in addition to the real and imaginary number lines? This is because some solutions blow up when there is a division ...
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### 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 ?
### 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 ...