ComplexNumber
AMC10/12
2005
A sequence of complex numbers $z_{0}, z_{1}, z_{2}, ...$ is defined by the rule
\[z_{n+1} = \frac {iz_{n}}{\overline {z_{n}}},\]
where $\overline {z_{n}}$ is the complex conjugate of $z_{n}$ and $i^{2}=-1$. Suppose that $|z_{0}|=1$ and $z_{2005}=1$. How many possible values are there for $z_{0}$?