Im

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

Im(z) gives the imaginary part of the number z.

Specific values

Specialized values

Values at fixed points

Values at infinities

General characteristics

Domain and analyticity

Im(z) is a nonanalytical function; it is a real-analytic function of the variable z.

Symmetries and periodicities

Parity

Im(z) is an odd function.

Mirror symmetry

Periodicity

No periodicity

Homogeneity

Transformations

Transformations and argument simplifications

Argument involving basic arithmetic operations

Addition formulas

Multiple arguments

Ratio of arguments

Power of arguments

Exponent of arguments

Products, sums, and powers of the direct function

Sums of the direct function

Complex characteristics

Real part

Imaginary part

Absolute value

Argument

Conjugate value

Signum value

Differentiation

Low-order differentiation

In a distributional sense for x∈ℝ .

Representations through equivalent functions

With related functions

With Re

With Abs

With Arg

With Conjugate

With Sign

Inequalities

Zeros

History

The function Im is encountered often in mathematics and the natural sciences.

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