If $|c|>2$ and $z_n=z_n-1^2+c$ with $z_0=0$ then $z_n rightarrow infty$
Clash Royale CLAN TAG #URR8PPP up vote 1 down vote favorite 1 Let $c in mathbbC$ and $f(z)=z^2+c$. Then define a sequence: $z_0=0$, $z_n=f(z_n-1)$ for all $n in mathbbN$. Show that $|c|>2 Rightarrow z_n rightarrow infty$. I had no clue which theorem I could use in this case in order to show this. I'd be thankful for any advice. complex-analysis share | cite | improve this question edited Aug 22 at 11:26 Did 243k 23 208 443 asked Aug 22 at 11:23 Thesinus 226 2 9 (Terrible title.) No need for a "theorem" here, just find a lower bound for $|z_n|$ in terms of $|z_n-1|$ and iterate. – Did Aug 22 at 11:26 2 Please refer to "escape criterion" here . – Ng Chung Tak Aug 22 at 18:25 add a comment  | up vote 1 down vote favorite 1 Let $c in mathbbC$ and $f(z)=z^2+c$. Then define a sequence: $z_0=0$, $z_n=f(z_n-1)$ for all $n in mathbbN$. Show that $|c|>2 Rig