Obtain the next iterate by plugging the previous iterate into the function.
First iterate:
[tex]z_0=2+i\implies z_1=f(z_0)=(2+i)^2-2-2i=1+2i[/tex]
Second iterate:
[tex]z_2=f(z_1)=(1+2i)^2-2-2i=-5+2i[/tex]
Third iterate:
[tex]z_3=f(z_2)=(-5+2i)^2-2-2i=19-22i[/tex]
Fourth iterate:
[tex]z_4=f(z_3)=(19-22i)^2-2-2i=-125-838i[/tex]
