[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

You can write any negative square root as i times a number. -1 is used to make things as simple as possible. For example take sqrt(-4):

sqrt(-4) = sqrt(-1)*sqrt(4) = 2i