# 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.

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