Awesome, glad you were able to explore! As the other reply mentioned, it actually turns out that all real (1d) signals are symmetric.
The key reason is in order for a circular path to stay on the real axis, it needs to be combined with another path rotating the opposite way, so their sum will stay on the x-axis.
The "opposite" rotation can be a negative frequency (1Hz vs -1Hz) or a very fast positive frequency (if you have a 12-hour clockface, 1 hour backwards = 11 hours forward, aka -1 (mod 12) = 11 (mod 12)). I'd like to explore this in the follow-up, glad you discovered it.
The key reason is in order for a circular path to stay on the real axis, it needs to be combined with another path rotating the opposite way, so their sum will stay on the x-axis.
The "opposite" rotation can be a negative frequency (1Hz vs -1Hz) or a very fast positive frequency (if you have a 12-hour clockface, 1 hour backwards = 11 hours forward, aka -1 (mod 12) = 11 (mod 12)). I'd like to explore this in the follow-up, glad you discovered it.