Presumably, you would start with a given initial value which can generally be chosen to be [tex]z_0=x+iy[/tex]. Then you would find [tex]z_3=f(z_2)=f(f(z_1))=f(f(f(z_0)))[/tex]. Symbolically, this expression will become quite cumbersome after just the first iteration.
So let's say [tex]z_0=1[/tex]. Then we have
[tex]z_1=f(1)=(1)^2-3+2i[/tex]
[tex]z_1=-2+2i[/tex]
[tex]z_2=f(-2+2i)=(-2+2i)^2-3+2i[/tex]
[tex]z_2=-3-6i[/tex]
[tex]z_3=f(-3-6i)=(-3-6i)^2-3+2i[/tex]
[tex]z_3=-30+38i[/tex]
