# Difference between revisions of "Hilger real part oplus Hilger imaginary part equals z"

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− | + | ==Theorem== | |

− | + | The following formula holds: | |

$$z = \mathrm{Re}_h(z) \oplus_h \mathring{\iota} \mathrm{Im}_h(z),$$ | $$z = \mathrm{Re}_h(z) \oplus_h \mathring{\iota} \mathrm{Im}_h(z),$$ | ||

where $\mathrm{Re}_h$ denotes the [[Hilger real part]] of $z$, $\mathrm{Im}_h$ denotes the [[Hilger imaginary part]] of $z$, $\oplus_h$ denotes the [[circle plus]] operation, and $\mathring{\iota}$ denotes the [[Hilger pure imaginary]]. | where $\mathrm{Re}_h$ denotes the [[Hilger real part]] of $z$, $\mathrm{Im}_h$ denotes the [[Hilger imaginary part]] of $z$, $\oplus_h$ denotes the [[circle plus]] operation, and $\mathring{\iota}$ denotes the [[Hilger pure imaginary]]. | ||

− | + | ||

− | + | ==Proof== | |

− | + | ||

− | + | ==References== | |

+ | |||

+ | [[Category:Theorem]] | ||

+ | [[Category:Unproven]] |

## Latest revision as of 21:42, 14 July 2016

## Theorem

The following formula holds: $$z = \mathrm{Re}_h(z) \oplus_h \mathring{\iota} \mathrm{Im}_h(z),$$ where $\mathrm{Re}_h$ denotes the Hilger real part of $z$, $\mathrm{Im}_h$ denotes the Hilger imaginary part of $z$, $\oplus_h$ denotes the circle plus operation, and $\mathring{\iota}$ denotes the Hilger pure imaginary.