y-length as part of a complex number

OB = 1
θ = .436332 (25°)

Cosine expressed in terms of y-length

Cosθ = cosh^-1[y-length]

= 2 / (e^ylength + e^-ylength)

Cosine expressed in terms of i

Cosθ = (e^iθ + e^-iθ) / 2

therefore

2 / (e^ylength + e^-ylength) = (e^iθ + e^-iθ) / 2

(e^ylength + e^-ylength)(e^iθ + e^-iθ) = 4

e^{ylength + iθ} + e^{ylength - iθ} + e^{-ylength + iθ} + e^{-ylength - iθ} = 4

e^{ylength + iθ} = e^ylength (Cosθ + iSinθ)

e^{ylength - iθ} = e^ylength (Cosθ - iSinθ)

e^{-ylength + iθ} = e^-ylength (Cosθ + iSinθ)

e^{-ylength - iθ} = e^-ylength (Cosθ - iSinθ)