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.

1st integer x

2nd integer x+1

3rd integer x+2

4th integer x+3

x+x+1 +x+2+x+3 =74

combine like terms

4x+6 = 74

subtract 6 from each side

4x = 68

x = 17

the integers are 17,18,19,20