How do I find the maximum value of $a$ such that $f(w) = w^2 + w$ is univalent in $|w|\lt a.$
I haven't a clue how to begin.
PS:
This is not a homework problem. It was assigned as a try problem.
Thanks.
How do I find the maximum value of $a$ such that $f(w) = w^2 + w$ is univalent in $|w|\lt a.$
I haven't a clue how to begin.
PS:
This is not a homework problem. It was assigned as a try problem.
Thanks.
Suppose $f(r)=f(s)$. That's $r^2+r=s^2+s$ $r^2+r+(1/4)=s^2+s+(1/4)$ $(r+(1/2))^2=(s+(1/2))^2$ $r+(1/2)=\pm(s+(1/2))$ The plus gets us nowhere, the minus gets us $r+s=-1$, so as long as $r+s=-1$ has no solutions in $|w|\lt a$, you're OK. So, how big can $r$ and $s$ be (in modulus), and still avoid solutions of $r+s=-1$?