Difference between revisions of "Hilger imaginary part"

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<center>{{:Hilger complex plane footer}}</center>

Latest revision as of 15:40, 21 January 2023

Let $h>0$ and let $z \in \mathbb{C}_h$, the Hilger complex plane. The Hilger imaginary part of $z$ is defined by $$\mathrm{Im}_h(z)=\dfrac{\mathrm{Arg}(zh+1)}{h},$$ where $\mathrm{Arg}$ denotes the principal argument of $z$ (i.e. $-\pi < \mathrm{Arg(z)} \leq \pi$).

Properties

Range of Hilger imaginary part
Limit of Hilger real and imag parts yields classical
Hilger real part oplus Hilger imaginary part equals z

References

Hilger complex plane and friends

$\Huge\mathbb{A}_h$
Hilger alternating axis
$\Huge\mathbb{I}_h$
Hilger circle
$\Huge\mathbb{C}_h$
Hilger complex plane
$\Huge\mathrm{Im}_h$
Hilger imaginary part
$\Huge\mathring{\iota}$
Hilger pure imaginary
$\Huge\mathbb{R}_h$
Hilger real axis
$\Huge\mathrm{Re}_h$
Hilger real part
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