[eli5] Why is imaginary number root -1? Why not root -n, since no number times each other would result in negative number?

Question

[eli5] Why is imaginary number root -1? Why not root -n, since no number times each other would result in negative number?

In: Mathematics

Answer 1

That’s because people chose i = sqrt(-1) as a basis for imaginary numbers, like 1 = sqrt(1) is the basis for real ones.