If it doesn’t exist, why and how do we use it?
In: Mathematics
Sqrt(-1) does not exist *in real numbers*, that is, there is no real number which produces -1 when squared. This makes the operation of square root feel weirdly incomplete in that you can’t apply it to any number you want, unlike other operations. So mathematicians started thinking: if the square root of a negative number like -1 cannot be found in any real numbers, what if we said that it’s an imaginary (that is, not real) number, namely i? Let’s make this assumption and see where it leads us. They then end up with complex numbers, which are things like A + B*i, that is, they consist of a real part A and an imaginary part B. And it turns out that these complex numbers are very neat, at least in that every complex number has a square root, but not only that. Complex numbers turned out to be so useful that electromagnetism theory, quantum theory and a load of other very important physics stuff simply does not work without them.
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