h-length as part of a complex number (page 2)

θ = .698131 (40°)
h-length of BA, relative to O, is .266515

e^{hlength + iθ} = e^hlength (Cosθ + iSinθ)
1.305407 (.766044 + i.642787)
= 1 + i.839099

e^{hlength - iθ} = e^hlength (Cosθ - iSinθ)
1.305407 (.766044 - i.642787)
= 1 - i.839099

If the h-length is measured from B to points of the vertical line (x = 1), relative to 0, and those values applied to the two complex expressions, the points generated, which are complex numbers, lie along the same vertical line passing through x = 1.