Answer
$1, -i, i$
Work Step by Step
This question asks for ALL zeros of the function
Given $P(x) = x^3 - x^2 + x - 1$
$P(x) = x^2 (x-1) + 1 (x-1)$
$P(x) = (x^2 + 1)(x-1)$
Set each polynomial equal to one
$x-1 = 0$
$x = 1$
$x^2 + 1 = 0$
$x^2 = -1$
$x = +/- i$
Thus the solutions are $1, -i, i$