# Hilger circle

Let $h>0$. The Hilger imaginary circle is defined by $$\mathbb{I}_h = \left\{ z \in \mathbb{C}_h \colon \left| z + \dfrac{1}{h} \right| = \dfrac{1}{h} \right\},$$ where $\mathbb{C}_h$ denotes the Hilger complex plane.