Prove that the subset $U = \{z : |z+ z^2|<1\}$ is open in the $\mathbb{C}$. This seems to be a simple question. But I am not getting anywhere with it.
What I have tried so far is this. If $w$ is in $U$, then I need to find $r >0$ such that the $B$ = ball centred at $w$ with radius $r$, lies inside $U$.
Now, let $w_1 \epsilon\ B$, then $|w_1 + w_1^2| \leq|w_1 - w| + |w + w^2| + |w^2 - w_1^2|$. So if I let $|w+w^2| = \delta <1$, then $|w_1 + w_1^2| \leq r + \delta + |w^2 - w_1^2|$.
I could possibly choose $r < 1-\delta$. But that does not help me do away with the last term on the right hand side of the inequality right? Or am I missing something obvious?