Answer
$\left\{1, -i, i\right\}$
Work Step by Step
The zeros of a function can be found by setting $y=0$ then solving the resulting equation.
Set $y=0$ then solve the equation to obtain:
\begin{align*}
0&=x^3-x^2+x-1\\
0&=(x^3-x^2)+(x-1)\\
0&=x^2(x-1)+(x-1)\\
0&=(x-1)\left[x^2+1\right]\\
\end{align*}
Use the Zero-Product Property by equating each factor to zero then solve each equation to obtain:
\begin{align*}
x-1&=0 &\text{or}& &x^2+1=0\\
x&=1 &\text{or}& &x^2=-1\\
x&=1 &\text{or}& &x=\pm\sqrt{-1}\\
x&=1 &\text{or}& &x=\pm i
\end{align*}
Thus, the zeros of the given function are: $\left\{1, -i, i\right\}$
