Find the limit at $\infty$ of the given function, or explain why it does not exist.
\begin{align*}
h(z)=\frac{z}{|z|^2}, z \neq 0
\end{align*}
\begin{align}
\lim_{z\to\infty} h(z) &=\lim_{z\to\infty} \frac{z}{|z|^2} \\
&=\lim_{z\to0}\frac{|z|^2}{z} && {\text{since z $\neq 0$}}\\
&=\lim_{z\to0} \frac{z\overline{z}}{z} \\
&=\lim_{z\to0} \overline{z}\\
&=\lim_{(x,y)\to(0,0)}x-iy \\
&=0
\end{align}
