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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)))).

 Dec 17, 2020
 #1
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-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.

 Dec 18, 2020

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