Solution
= Solution
The <Koebe quarter theorem> says that if $F:\mathbb D\to\mathbb C$ is a <univalent function> with $F(0)=0$ and $F'(0)=1$, then
$$
\boxed{\{w:|w|<1/4\}\subseteq F(\mathbb D).}
$$
Equivalently, an arbitrary <univalent function> $f$ on the <unit disc> has $B(f(0),|f'(0)|/4)\subseteq f(\mathbb D)$. The constant cannot be increased: the <Koebe function> $F(w)=w/(1-w)^2$ omits the ray $(-\infty,-1/4]$.