Fungrim symbol: Im

Symbol: Im —

\operatorname{Im}(z)

— Imaginary part

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

Table data:

\left(P, Q\right)

such that

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

Definitions:

Fungrim symbol	Notation	Short description
`Im`	$\operatorname{Im}(z)$	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 39 topics:

Illustrations of Jacobi theta functions (in 19 entries)
Lambert W-function (in 8 entries)
Square roots (in 7 entries)
Barnes G-function (in 7 entries)
Specific values of Carlson symmetric elliptic integrals (in 6 entries)
Natural logarithm (in 6 entries)
Inverse tangent (in 6 entries)
Illustrations of Eisenstein series (in 6 entries)
Exponential function (in 6 entries)
Coulomb wave functions (in 6 entries)
Complex parts (in 6 entries)
Series and product representations of Jacobi theta functions (in 5 entries)
Weierstrass elliptic functions (in 4 entries)
Zeros of the Riemann zeta function (in 3 entries)
Specific values of the digamma function (in 3 entries)
Sine (in 3 entries)
Riemann zeta function (in 3 entries)
Sinc function (in 2 entries)
Jacobi theta functions (in 2 entries)
Imaginary unit (in 2 entries)
Hurwitz zeta function (in 2 entries)
Gamma function (in 2 entries)
Eisenstein series (in 2 entries)
Dirichlet L-functions (in 2 entries)
Digamma function (in 2 entries)
Carlson symmetric elliptic integrals (in 2 entries)
Bessel functions (in 2 entries)
Airy functions (in 2 entries)
Powers (in 1 entries)
Modular transformations (in 1 entries)
Modular lambda function (in 1 entries)
Modular j-invariant (in 1 entries)
Keiper-Li coefficients (in 1 entries)
Error functions (in 1 entries)
Confluent hypergeometric functions (in 1 entries)
Complex plane (in 1 entries)
Catalan's constant (in 1 entries)
Bell numbers (in 1 entries)
Arithmetic-geometric mean (in 1 entries)

Entries using this symbol

The symbol Im appears in 131 entries: