>>12856395complex numbers are an expansion of the reals
think of it like this: you have a process that needs explaining, but the numbers you have are not enough to do it
for example - you have 2 people that you need to feed with 1 apple, so you cut it in half and both people get fed
now, what happened to the apple? you had 1, and used something that's less than 1 to feed two people equally. but the number that's less than 1 is 0, how can you feed someone with 0 of something? ignoring that, does this mean that if we take 0 two times we get 1? we could feed 4 people with that apple, so 0 four times would be 1 too? and 5, and 6, and 128??? what the hell???
as you can see, lots of logical problems arise if you try to explain what just happened with whole numbers.
so, in order to adequately explain what's going on in the real world, you say "alright well since there's clearly many ways we can use less than 1 of something, let's write it down as 1/y, where y is the number of uses we got out of the 1"
then, after thinking a bit, you go "ah but we can use more than 1 too, right?" and change that to x/y where x is the number of things you used for y uses
then, after playing around with the new expression for a bit, you discover that if you use 6 apples to feed 3 people, they get 2 apples each, and you have a realization that your new expression x/y doesn't just apply to these "new" things you try to describe with the expression, but also to the whole numbers! in fact, every whole number can be described with infinitely many of these expressions!
and so, you arrive at the point where these things (that you decided to call "fractions") are more fundamental to the universe than whole numbers, giving you the abiliy to describe a larger set of phenomena
complex (imaginary) numbers are a similar case, being an expansion of the reals, used to solve things that are "impossible" to solve using just the reals, like all polynomial equations instead of only some of them
