highschool:complex numbers?

i isn't a number like 5 or -8 or 0 or even infinity, that is, it doesn't go on the number line. It isn't bigger than 5, or less than 5, or 5, it's not on the same type of scale. Undefined means that there is no answer, the word undefined isn't an answer in itself. The square root of -1 has an answer, but no answer between negative infinity and infinity. You can't count to i, or say "there are i birds on earth" or use it in any way in that sense, but it does exist. Infinity isn't a number, it is a concept. It is used to mean "the end of the number line" even though the number line is endless on both the positive and negative sides, and in that way infinity doesn't actually exist. However, i exists, just not on the number line, think of it as off to the side of the number line, going further off to the side as it becomes more "i-like" (or imaginary), like 5i is further off to the side than 2i, and 0i is just 0, which is on the number line, so that is where the "real" number line and the "imaginary" number line cross, like a graph where the x and the y cross.

I guess working through problems involving infinity is not as abstract as analyzing the imaginary numbers complex planes, especially if you are going for an electrical engineering discipline.

It has to be i bcaus when you are going to multiply sqrt -1 by itself the answer comes to 1 or -1 so for such cases u are being taught to use i now.