How come there isn’t an imaginary system for dividing a number by 0, while there is one for taking the square root of a negative number?
In: Mathematics
Taking the square root of an imaginary number works within regular math. The imaginary number i is just equal to the sqrt(-1), which algebraically is a-ok so long as it doesn’t need to be evaluated. You can do useful math using i and it’s not a whole new system.
Dividing by zero just makes no sense. How many groups of 0 can you make out of x number of items? (A way of thinking about division). The answer is infinite- or maybe it’s 0? Maybe there’s 1 group, but no matter what it’s up for debate (to some extent) and dividing by zero, algebraically, is not useful. Also, if you could divide by zero, you can prove that any number x is equal to any number y, and x and y could be -39104 and 2 respectively
tl;dr: imaginary numbers follow the rules of algebra. Dividing by zero is against the rules because the result just can’t be determined, and it wouldn’t be a useful system
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