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.

Practice the set Target JEE_Advanced - 2015 and boost up your preparation.

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