Euler Orbit Properties
Time / Angle θ:
1.00 rad
Real (cos θ):
0.540
Imaginary (sin θ):
0.841
Position Z = e^(iθ):
0.54 + 0.84i
Velocity V = iZ:
-0.84 + 0.54i
Speed |V| = |iZ|:
1.000 (constant)
The orbit Z(t) = e^{it} starts at 1.
Its velocity vector is always V = iZ, which is perpendicular to Z (pointing tangentially) and has a constant magnitude of 1.00.
Therefore, after time t = θ, the particle travels a distance of θ along the circle, arriving at cos θ + i sin θ.