+0

# help):

+1
58
3
+188

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
+2

Composite functions,

First, we solve the inside then, the outside using the given information.

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
#3
+188
0

thank you! :)

atlas9  Jan 2, 2020