For all complex numbers z, let
f(z) = z^2 if z is not real
f(z) = -z^2 if z is real.
Find f(f(f(f(-i)))).
+421 -i is not real. Thus, we square it. -i^2 = i^2 =-1. -1 is real. Thus, we square 1. After a whole chain of squaring 1 and -1, we end up eventually with 1, so the answer is 1.
