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For all complex numbers z, let

f(z) = z^2 if z is not real

f(z) = z^3 if z is real

Find f(f(f(f(1+i)))).

 Mar 6, 2022
 #1
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\((1+i)^2 = i^2+2i+1 = -1 + 2i +1 = 2i\)

\((2i)^2 = 4i^2 = 4 \times -1 = -4\)

\(-4^3 = -64\)

\(-64^3 = \color{brown}\boxed{-262,144}\)

.
 Mar 7, 2022

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