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

(In reply to computer assisted solution by Charlie)

The three cycle can be verified by evaluating the compositions G(G(z)) and G(G(G(z))).

Posted by Brian Smith on 2016-04-13 23:15:18