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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 \(f(f(f(f(1+i))))\).

 Jan 2, 2020
 #1
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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.

 Jan 2, 2020
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thank you! :)

atlas9  Jan 2, 2020

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