Find the three output values of the fractal-generating function

Question

F(z)= z²-i

 

use z=1 as the first input value. 

Answer 1

F(z) = z² - i, where z is complex.

 

 

z = 1:

 

  F(1) = 1² - i = 1 - i

 

 

z = 1 - i:

 

  F(1 - i) = (1 - i)² - i = (1 - i)(1 - i) - i = (1 - i - i + i²) - i

 

= (1 - 2i - 1) - i = -3i

 

 

z = -3i:

 

  F(-3i) = (-3i)² - i = 9i² - i = -9 - i