I am given ( a simplistic definition I think ) of Mandelbrot set:
M- set of complex numbers $c \in \mathbb{C}$ s.t. the sequence $(z_n)$ is bounded where $z_0=0 , z_{n+1}=z_n^2+c $
Need to show that:
(i)$-2\in M$
(ii) $1/4 \in M$.
Am I missing something here or is it kind of trivial?
(i) $ c=-2 $ gives $z_n=2 \space \forall n\geq 2$ , obviously bounded so $c \in M$ ?
(ii) $c=1/4$ we get that $z_n \longrightarrow \frac{1}{2} $ again bounded.
Am I doing it right or did I completely miss somehow the point of the exercise? It just seems too simple to be true. Sorry if this is a stupid question, I have never worked with Mandelbrot set before.