Frequency Conversion Product Lower than 0 Hz (Negative Frequency?)
negative frequency is PHASE ROTATION of the other direction.

Had to assist in synthesizing GSM signals, some decades back. We soon understood we could produce whatever signals we wanted, using I+Q mixers followed by summation.

Frequency is typically the derivative of phase, and phase is the X in sin(X).

X typically is 2 * PI * Frequency * Time.

Since we don't reverse time, we do use ( -Frequency) and thus have a negative phase trajectory.