Definition: A set S in $\mathbb{C}$ is called a star domain if there exists an $a \in S$ such that for all $x \in S$, the line segment from a to x is in S. And the point $a \in S$ is called a star center of the star domain.
a) $\{z \in \mathbb{C}: z\neq x+0i, \textrm{ where } |x|\geq 1\}$
Someone told me that this is a star domain and has a star center, however, I do not really see it. My understanding that it is the line segments that are not joined together. How would I prove existence of a star domain?
The graph is the whole plane excluding 2 line segments y=0 from (1,$\infty)$ and (-1,$\infty$)