AMC 12B 2005 Problem 22

A sequence of complex numbers z_{0}, z_{1}, z_{2}, \ldots is defined by the rule

z_{n+1}=\dfrac{i z_{n}}{\overline{z_{n}}}

where \overline{z_{n}} is the complex conjugate of z_{n} and i^{2}=-1. Suppose that \left|z_{0}\right|=1 and z_{2005}=1. How many possible values are there for z_{0} ?

Answer Choices
A. 1
B. 2
C. 4
D. 2005
E. 2^{2005}