Question

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

a. 2+i, 2+5i, -2595+205i
b. 2+i, 5+5i, -2595+205i
c. 2+i, 5+5i, 2+51i
d. 5+5i, 2+51i, -2595+205i

Answer 1

We can use the multiple choices to tell us the initial value. Let z_0 = 2 + i . now find
f(2 + i )

Answer 2

how do i do that? sorry i dnt know im prettty slow

Answer 3

oh wow

Answer 4

ok

Answer 5

whats next

Answer 6

Suppose the first term is 2 + i, then the second term is f(2 + i )
$$
\Large {
f(2+i) = (2+i)^2 + 2 + i \\= (2+i)(2+i) + 2 + i
\\=2^2 + 2i + 2i + i^2 + 2 + i
\\ = 4 + 4i + (-1) + 2 + i
\\ = 5 + 5i
}
$$

Answer 7

now take this value and plug into f(z)