h-length as part of a complex number (page 1)

OB = 1
OB and OB₂ are segments on the x-axis
the y-axis intersects O at the origin

Cosine expressed in terms of h-length

Cosθ = e^-hlength


Cosine expressed in terms of i

Cosθ = (e^iθ + e^-iθ) / 2


therefore

(e^iθ + e^-iθ) / 2 = 1 / e^hlength

e^hlength (e^iθ + e^-iθ) = 2

e^{hlength + iθ} + e^{hlength - iθ} = 2


e^hlength (Cosθ + iSinθ) + e^hlength (Cosθ - iSinθ) = 2