+0  
 
-1
73
2
avatar+229 

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 $f(f(f(f(1+i))))$

 Feb 18, 2021
 #1
avatar
0

We use the rule of at each step

f(f(f(f(1 + i))))

= f(f(f(2 + 2i)))

= f(f(-8i))

= f(64)

= -4096.

 Feb 18, 2021
 #2
avatar+31264 
+1

f(1+i) =     (1+i)^2 = 1 + 2i + i^2 = 2i

 

f(2i) =( 2i)^2 = -4

f(-4) = - ( -4^2) = -16

f(-16)  = - (-16)^2 = - 256

 Feb 18, 2021

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