Find the first three iterates of the function f(z) = z2 + c with a value of c = 2 - 3i and an initial value of z0 = 1 + 2i. a. -1 + i, 2 - 3i, -17 - 29i c. 1 + i, 2 + 3i, -17 - 29i b. -1 + i, 2 - 5i, -19 - 23i d. 1 + i, 2 + 3i, -19 - 23i

Find the first three iterates of the function f(z) = z^2 + c with a value of c = 2 - 3i and an initial value of z0 = 1 + 2i. 
We assume that f(z) is an iterative function such that

where z0 has been given as 1+2i.

We have c=2-3i, =>
f(z)=z²+2-3i

Iterations:
z1=f(z0)=f(1+2i)=(2i+1)^2-3i+2=1-4+4i-3i+2=i-1
z2=f(z1)=f(i-1)=(i-1)^2-3i+2=-1+1-2i-3i+2=2-5i
z3=f(z2)=f(2-5i)=(2-5i)^2-3i+2=4-25-20i-3i+2=-23i-19

There is one answer choice that matches the above, and will be left for you to choose the right choice.  Recall that the above list of answer choices are not listed in order a,b,c,d  but in the order a,c,b,d.  Please double-check answer choices before deciding.