[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

sqrt(-1) is the part that can’t be simplified but you can factor it out of anything. sqrt(-n) is simply sqrt(-1 * n) and sqrt(a * b) = sqrt(a) * sqrt(b) so you’d get sqrt(-1) * sqrt(n).