What is the polynomial function of lowest degree with leading coefficient 1 and roots 1 and 1 plus i ?

For a polynomial with real coefficients, a non-real root 1 + i requires its conjugate 1 − i to be a root as well. The lowest-degree monic polynomial is therefore (x − 1)(x − (1 + i))(x − (1 − i)) = (x − 1)((x − 1)² + 1). Expanding gives x³ − 3x² + 4x − 2, which is choice A.

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