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)))).
1 + i is not real, so f(1 + i) = (1 + i)2 = 12 + 2i + i2 = 1 + 2i - 1 = 2i
2i is not real, so f( f(1 + i) ) = f(2i) = 4i2 = -4
-4 is real, so f( f( f(1 + i) ) ) = -(-4)2 = -16
-16 is real, so f( f( f( f(1 + i) ) ) ) = -(-16)2 = -256
thank you so much!!!!
+865 
