The answer is no! In this video, I show that there is no way to compare the complex numbers in a way that 3 very natural properties are satisfied. Enjoy!
Note: There's a small mistake in the video. When I write c is positive 0 in property 3, I don't mean c positive 0 as a real number, but c positive 0 with the new ordering squiggly greater than (so it should be c squiggly greater than 0).
