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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)))).

 Jun 19, 2020
 #1
avatar+21955 
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1 + i  is  not real, so  f(1 + i)  =  (1 + i)2  =  12 + 2i + i2  =  1 + 2i - 1  =  2i

 

2i  is  not real, so  f( f(1 + i) )  =  f(2i)  =  4i2  =  -4

 

-4  is  real, so  f( f( f(1 + i) ) )  =  -(-4)2  =  -16

 

-16  is  real, so  f( f( f( f(1 + i) ) ) )  =  -(-16)2  =  -256  

 Jun 19, 2020
 #2
avatar+794 
0

thank you so much!!!!

AnimalMaster  Jun 19, 2020

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