Sequence of Complex Stuff

Algebra Level 4

x1=0,  and  xn+1=xn2i   for  n>1\large x_1=0, \ \ \text{and} \ \ x_{n+1}=x_n^2-i \ \ \text{ for} \ \ n>1

Above is the sequence x1,x2,x3,x_1,x_2,x_3, \ldots of the complex numbers.. Find the square of the distance between x2000x_{2000} and x1997x_{1997} in the complex plane.

Details and Assumptions:
i=1 i = \sqrt{-1} is the imaginary number.


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