Fungrim symbol: Im

Symbol: Im —

\operatorname{Im}\!\left(z\right)

— Imaginary part

Domain	Codomain
$z \in \mathbb{R}$	$\operatorname{Im}\!\left(z\right) \in \left\{0\right\}$
$z \in \mathbb{C}$	$\operatorname{Im}\!\left(z\right) \in \mathbb{R}$

Table data:

\left(P, Q\right)

such that

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

Definitions:

Fungrim symbol	Notation	Short description
`Im`	$\operatorname{Im}\!\left(z\right)$	Imaginary part
`RR`	$\mathbb{R}$	Real numbers
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("9086c6"),
    SymbolDefinition(Im, Im(z), "Imaginary part"),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(Element(z, RR), Element(Im(z), Set(0))), Tuple(Element(z, CC), Element(Im(z), RR)))))

Topics using this symbol

The symbol Im appears in 20 topics:

Lambert W-function (in 8 entries)
Square roots (in 7 entries)
Inverse tangent (in 6 entries)
Coulomb wave functions (in 6 entries)
Natural logarithm (in 5 entries)
Exponential function (in 5 entries)
Complex parts (in 5 entries)
Weierstrass elliptic functions (in 4 entries)
Zeros of the Riemann zeta function (in 3 entries)
Sine (in 3 entries)
Riemann zeta function (in 3 entries)
Gamma function (in 2 entries)
Bessel functions (in 2 entries)
Airy functions (in 2 entries)
Powers (in 1 entries)
Modular transformations (in 1 entries)
Modular j-invariant (in 1 entries)
Error functions (in 1 entries)
Confluent hypergeometric functions (in 1 entries)
Complex plane (in 1 entries)

Entries using this symbol

The symbol Im appears in 65 entries: