What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 + i?

x³ - 3x² + 4x - 2

complex roots occur in conjugate pairs

1 + i is a root then so is 1 - i

the factors of the polynomial are therefore

f (x) = (x - 1) (x - (1 + i)) (x - (1 - i))

= (x - 1) (x² - 2x + 2) (expand factors and simplify)

= x³ - 3x² + 4x - 2

f (x) = x3 - 3x2 + 4x - 2