Question 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 $|z_0| = 1$ and $z_{2005} = 1.$ How many possible values are there for $z_0?$
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 $|z_0| = 1$ and $z_{2005} = 1.$ How many possible values are there for $z_0?$