Answer
$-4z\textbf{j}$
Work Step by Step
curl $\textbf{F}=\nabla\times\textbf{F}=\nabla\times\langle x^{2}-z^{2},1,2xz\rangle$
$=(\frac{\partial (2xz)}{\partial y}-\frac{\partial (1)}{\partial z})\textbf{i}+(\frac{\partial(x^{2}-z^{2})}{\partial z}-\frac{\partial(2xz)}{\partial x})\textbf{j}+(\frac{\partial(1)}{\partial x}-\frac{\partial(x^{2}-z^{2})}{\partial y})\textbf{k}$
$=(0-0)\textbf{i}+(-2z-2z)\textbf{j}+(0-0)\textbf{k}$
$=-4z\textbf{j}$
