The Measurement-Line Helix Phase Angle Imaginary: A Complex Reading of the Phase Advancement of the Measurement-Line Helix

This paper introduces the concept of the "measurement-line helix phase angle imaginary": it is the phase factor U(Theta)=e^{i*Theta} read from the continuous phase advancement of the measurement-line helix on its horizontal projection complex plane. The imaginary unit i, the mirror factor -i, and the half-turn point -1 are not independently assigned algebraic symbols. They are readings of this continuous family at periodic division points: 90 degrees, 270 degrees, and 180 degrees respectively. In particular, one mirror operation of the reverse measurement-line helix corresponds to a phase retreat of 90 degrees, reading -i; two mirror operations read -1. This gives the geometric origin of i^2=-1. Keywords: measurement-line helix phase angle imaginary; measurement-line helix; mirror factor; quarter-period; self-referential measurement