> Why don't we just use vectors and make math easier to learn?
We do just use vectors; over complex numbers. You really want both, where the vectors themselves are made up of[1] complex numbers. Using a single complex number to represent a vector has gone out of style in some sense because it's restricted to two dimensions. For example historically it was quite common to represent the velocity of a fluid at each point with a complex number. While you can do this, and there are many of advantages, most don't generalize to higher dimensions.
Complicated math concepts (like differential equations) are much easier to learn with a solid background in complex numbers. Vectors are important, but so are complex numbers.
