Consider the function:
G(Z) = (Z+i)/(Z-i) for all complex numbers Z ≠ i, and:
The sequence {Z_n} is defined as:
G(Z_n-1) = Z_n, whenever n is a positive integer, and:
Z₀ = 1/137 + i

Find each of A, B, C and D, given that:
Z₂₀₁₄ = A+B*i, and:
Z₂₀₁₅ = C+D*i