For all complex numbers z, let \( f(z) = \left\{ \begin{array}{cl} z^{2}&\text{ if }z\text{ is not real}, \\ -z^2 &\text{ if }z\text{ is real}. \end{array} \right.\) Find f(f(f(f(1+i)))).
Here is how can we compute the answer:
f(f(f(f(1+i) = f(f(f((1+i)^2) = f(f(f(0) = f(f(0) = f(0) = 0
Therefore, the answer is 0.