All about actions about groups of things that can exhibit some form of symmetry
Abstract algebra (aka “modern algebra”) deserves its name, it’s abstract. It’s about the kinds of actions you can do on some “group”, where a group is just a set of elements that have some form of relation, that preserve in inner structure of the group.
There is a group called “the number line”.
Addition is a symmetric operation on a number line. It slides the number line positive and negative.
Multiplication is a symmetric operation on a number line that stretches it. It stretches out when multiplying by numbers greater than 1, and shrinks it when multiplying by numbers less than 1.
Adding complex numbers slides the complex plane up or down (up for i, down for -i).
Multiplying complex numbers rotates the complex plane about the origin. Clockwise for i, counterclockwise for -i. “how much” it’s rotated, I don’t fully grasp, but its in radians as you might expect.