Task 218
Task 218: test task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. Let $F(z)=\frac{z+i}{z-i}$ for all complex numbers $z\not= i,$ and let $z n=F(z {n-1})$ for all positive integers $n.$ Given that $z 0=\frac 1{137}+i,$ find $z {2002}.$
The task
Let $F(z)=\frac{z+i}{z-i}$ for all complex numbers $z\not= i,$ and let $z_n=F(z_{n-1})$ for all positive integers $n.$ Given that $z_0=\frac 1{137}+i,$ find $z_{2002}.$