Given that \(x - \frac{1}{x} = i \sqrt{2},\) find \(x^{2187} - \frac{1}{x^{2187}}\)
x - 1/x =i*sqrt(2)
x^2187 - 1 / (x^2187) =
x^(2187+2187) - 1 / (x^2187) - Use substitution
(x^4374 - 1) / (x^2187) =i*sqrt(2)
