Fungrim symbol: Arg

Symbol: Arg —

\arg\!\left(z\right)

— Complex argument

Domain	Codomain
$z \in \mathbb{R}$	$\arg\!\left(z\right) \in \left\{0, \pi\right\}$
$z \in \mathbb{C}$	$\arg\!\left(z\right) \in \left(-\pi, \pi\right]$
$z \in \left\{\infty\right\}$	$\arg\!\left(z\right) \in \left\{0\right\}$
$z \in \left\{-\infty\right\}$	$\arg\!\left(z\right) \in \left\{\pi\right\}$

Table data:

\left(P, Q\right)

such that

\left(P\right) \implies \left(Q\right)

Definitions:

Fungrim symbol	Notation	Short description
`Arg`	$\arg\!\left(z\right)$	Complex argument
`RR`	$\mathbb{R}$	Real numbers
`ConstPi`	$\pi$	The constant pi (3.14...)
`CC`	$\mathbb{C}$	Complex numbers
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("b7d740"),
    SymbolDefinition(Arg, Arg(z), "Complex argument"),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(Element(z, RR), Element(Arg(z), Set(0, ConstPi))), Tuple(Element(z, CC), Element(Arg(z), OpenClosedInterval(Neg(ConstPi), ConstPi))), Tuple(Element(z, Set(Infinity)), Element(Arg(z), Set(0))), Tuple(Element(z, Set(Neg(Infinity))), Element(Arg(z), Set(ConstPi))))))

Topics using this symbol

The symbol Arg appears in 5 topics:

Complex parts (in 10 entries)
Powers (in 5 entries)
Square roots (in 4 entries)
Natural logarithm (in 3 entries)
Exponential function (in 1 entries)

Entries using this symbol

The symbol Arg appears in 23 entries: