# Circle plus

From timescalewiki

Let $h>0$ and $z_1,z_2 \in \mathbb{C}_h$, the Hilger complex plane. Then we define the $\oplus_h$ operation by $$z_1 \oplus_h z_2 = z_1+z_2+z_1 z_2h.$$

# Properties

Regressive functions form an abelian group under circle plus

Circle minus inverse of circle plus

Hilger real part oplus Hilger imaginary part equals z