A lot of the comments answer why we have them but an interesting thing is the way they came up with them (from what I remember). Basically, math always evolves, and mathematicians were at a crossroads trying to figure out problems. They needed a number that when it was squared resulted in a negative number. Previously thought impossible because squares can only be positive numbers. What’s the answer? Create a new “imaginary number” that solves your problem, and it leads to many different applications and uses in modern mathematics. Always a complicated topic to think about though!