How do you find iterates of a function?

For example, two problems I have are:
1) Find the first three iterates of the function f(Z) = Z^2 + 2 + i , when Z base 0 = 2 + 2i.

2) Find the third iterate of the function f(t) = 9t - 3 when t base 0 = 1/3 + i/9.

Question

How do you find iterates of a function?

For example, two problems I have are:
1) Find the first three iterates of the function f(Z) = Z^2 + 2 + i , when Z base 0 = 2 + 2i.

2) Find the third iterate of the function f(t) = 9t - 3 when t base 0 =  1/3 + i/9.

kc_kennylau · Answer

$$Z_1=Z_0^2+2+i$$

kc_kennylau · Answer

$$Z_1=Z_0^2+2+i=(2+2i)^2+2+i$$

loser66 · Answer

z1 = f(z0)
z2 = f(z1)
z3=f(z2)
that's it. just compute one by one

anonymous · Answer

i would use a calculator

anonymous · Answer

$$z_1=(2+2i)^2+2+i=2+9i$$ http://www.wolframalpha.com/input/?i=%282%2B2i%29^2%2B2%2Bi

anonymous · Answer

$z_2=(2+9i)^2+2+i=-75+37i$ http://www.wolframalpha.com/input/?i=%282%2B9i%29^2%2B2%2Bi

anonymous · Answer

should be clear how to do the next one right?

anonymous · Answer

oooohhhhh, i see what you mean! :D Okay, yes, that makes sooo much sense. Thank you, thank you, thank you!! ♥

anonymous · Answer

yw $\heartsuit$