Difference between revisions of "Forward circle plus"
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Let $h>0$ and $z_1,z_2 \in \mathbb{C}_h$, the [[Hilger complex plane]]. Then we define the $\oplus_h$ operation by | Let $h>0$ and $z_1,z_2 \in \mathbb{C}_h$, the [[Hilger complex plane]]. Then we define the $\oplus_h$ operation by | ||
$$z_1 \oplus_h z_2 = z_1+z_2+z_1 z_2h.$$ | $$z_1 \oplus_h z_2 = z_1+z_2+z_1 z_2h.$$ | ||
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</div> | </div> | ||
</div> | </div> | ||
| − | + | [[Circle minus inverse of circle plus]]<br /> | |
| − | + | [[Hilger real part oplus Hilger imaginary part equals z]]<br /> | |
Revision as of 21:34, 14 July 2016
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
Theorem: The structure $(\mathbb{C}_h,\oplus_h)$ is an Abelian group.
Proof: █
Circle minus inverse of circle plus
Hilger real part oplus Hilger imaginary part equals z
