# Sequence of Complex Stuff

**Algebra**Level 4

\[\large x_1=0, \ \ \text{and} \ \ x_{n+1}=x_n^2-i \ \ \text{ for} \ \ n>1\]

Above is the sequence \(x_1,x_2,x_3, \ldots\) of the complex numbers.. Find the square of the distance between \(x_{2000}\) and \(x_{1997}\) in the complex plane.

**Details and Assumptions:**

\( i = \sqrt{-1} \) is the imaginary number.