Quantum spin is a mathematical construct applied to elementary particles like photons or electrons. It is called imaginary because an electron is a particle with no size so it can’t actually spin, and if it had a size, its edges would have to move faster than light to explain the observed spin rate. Current physics then calls quantum spin imaginary because photons and electrons are points with no extent but this model extends their vibration outside our space in reality, so a photon is a 2D sine wave generated in a complex plane that actually does spin on its movement axis.
QR3.7.1. The Curious Case of Quantum Spin
QR3.7.2. Quantum Directions
QR3.7.3. Polarization