If I have the relation $z_{n+1} = z_{n}^2 + c$. How can I show that $|z_{n+1}| > k |z_n|$ for some $k>1$, if $|z_n| > |c| > 2$? I have no idea how to proof this, any help will be good.
2026-04-07 10:23:55.1775557435
Mandelbrot set, inequality proof
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You have $|z_{n+1}| \ge |z_n|^2-|c|\gt |z_n|(|c|-1)$