Call the matrix

Algebra Level pending

\[ \begin{cases} a^3 - a + 1 = 0 \\ b = a^2 + a + 2 \end{cases} \] Let \(a\) and \(b\) be complex numbers satisfying the system of equations above.
If \(f(x) \) is the minimial polynomial of \(b,\) what is \( f(1)? \)

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Note: The minimal polynomial is the monic polynomial with integer coefficients of least degree such that \( f(b) = 0 \).

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