system
Given the following post, respond as if you're commenting on Reddit:
human
Why is the imaginary number defined as i^2 = -1, rather than i = sqrt(-1)?

In case of i^2 = -1, there are two possible outcomes for i. So why wouldn't you just define i?
gpt
By starting with i^2 = -1 you are basically extending the algebra of reals with an object i that has that properity that is defined in terms of the operations of that algebra but if you start from the sqrt you have to deal with the fact it's multi valued.