+262 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 \(f(f(f(f(1+i))))\).
Composite functions,
First, we solve the inside then, the outside using the given information.
so start with:
f(1+i) ,given f(z)=z^2 if z is not real well it is not real here so we square it.
\((1+i)^2\)=\(2i\)
next f
f(2i) , well it is still imaginary and not real so square it again
\((2i)^2=-4\)
next f
f(-4) now it is real, so -z^2
\(--4^2=16\)
2 negatives give positive.
Now the last f
f(16) , it is real so
\(-16^2=-256\) answer.
