For complex numbers z, let [tex] \[f(z) = \left\{
\begin{array}{cl}
z^{2}&\text{ if }z\text{ is not real}, \\
z+2 &\text{ if }z\text{ is real}.
\end{array}
\right.\] [/tex]

Find [tex] f(i)+f(1)+f(-1)+f(-i) [/tex].