I have no math experience or education, so please let me know if this is useless. But I realized you could express real numbers as rotations. Here’s my thought process.
Real Rotation
Real numbers can be thought of as rotations around the unit circle, with a single rotation equaling the unit. Any real number x can then be expressed in the form e^(x2 πi) on the complex plane. Positive numbers rotate counter-clockwise a certain number of times (or alternatively a certain number of revolutions per second), and negative numbers rotate in the opposite direction. This is real rotation.
To represent imaginary numbers using real rotation, you would simply replace x with yi. Any imaginary number is expressed in the form e^(yi(2 πi)) which simplifies to e^(-2 πy). This of course cannot be graphed on the complex plane except as a 1-d position on the real number line, but it can be represented on the real plane as an exponential function. Imaginary numbers in real rotation decay extremely rapidly for higher values of y, and grow rapidly in the negative direction for lower values of y.
Complex numbers can also be represented through real rotation in the form e^((ai+b)(2 πi)) which simplifies to (e^(-2 πa))*(e^(2 πib)). b thus determines rotation, and a determines magnitude of the unit circle. For higher values of a the magnitude shrinks rapidly, whereas for lower values it grows rapidly.
Again, I just did this for fun, but I’m wondering if it’s at all useful. I find it interesting that imaginary and real numbers swap coordinate planes, but complex numbers stay where they are (though their behavior changes dramatically.)