Find the first three output values of the fractal generating function f (z) = z2 + 2 + i.

A. 2 + i, 5 + 5i, - 2595 + 205i

B. 2 + i, 2 + 51i, - 2595 + 205i

C. 2 + i, 5 + 5i, 2 + 51i

D. 5 + 5i, 2 + 51i, - 2595 + 205i

A fractal generating function is given by

f (z) = Z² + 2 + i

→f (0) = 0² + 2 + i

= 2 + i

→f (2+i) = (2+i) ² + 2 + i →Use identity (a+b) ² = a² + b² + 2 a b

and i² = - 1

= 4 + 4 i - 1 + 2 + i

= 5 + 5 i

Now→, f (5 + 5 i) = (5 + 5 i) ² + 2 + i →Use identity (a+b) ² = a² + b² + 2 ab

and i² = - 1

= 25 - 25 + 50 i + 2 + i

= 51 i + 2

→So, f (0) = 2 + i, f (2 + i) = f (5 + 5 i) = 2 + 51 i

→Option C, 2 + i, 5 + 5 i, 2 + 51 i are the first three output of fractal generating function f (z) = z² + 2 + i.