Minimal Polynomial

Algebra Level 5

Let \(\alpha = i-\sqrt{2}\), where \(i = \sqrt{-1}\), and \( f(x) \) be the minimal polynomial of \( \alpha \). That is, \( f(x) \) is a monic polynomial with rational coefficients of smallest possible nonzero degree such that \( f(\alpha) = 0 \).

Find \( f(1) \).

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