Answer
$\left\{-2, 2, -2i, 2i\right\}$
Work Step by Step
The zeros of a function can be found by setting $f(x)=0$ then solving the resulting equation.
Set $f(x)=0$ then solve the equation to obtain:
\begin{align*}
0&=x^4-16\\
0&=(x^2-4)+(x^2+4)\\
0&=(x-2)(x+2)(x^2+4)\\
\end{align*}
Use the Zero-Product Property by equating each factor to zero then solve each equation to obtain:
\begin{align*}
x-2&=0 &\text{or}& &x+2=0& &\text{or}& &x^2+4=0\\
x&=2 &\text{or}& &x=-2& &\text{or}& &x^2=-4\\
x&=2 &\text{or}& &x=-2& &\text{or}& &x=\pm\sqrt{-4}\\
x&=2 &\text{or}& &x=-2& &\text{or}& &x=\pm2i\\
\end{align*}
Thus, the zeros of the given function are: $\left\{-2, 2, -2i, 2i\right\}$
