I

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

Specific values

General characteristics

The imaginary unit i is a constant. It is the pure complex niumber.

Complex characteristics

Real part

Imaginary part

Absolute value

Argument

Conjugate value

Signum value

Differentiation

Low-order differentiation

Fractional integro-differentiation

Integration

Indefinite integration

Integral transforms

Fourier exp transforms

Inverse Fourier exp transforms

Fourier cos transforms

Fourier sin transforms

Laplace transforms

Inverse Laplace transforms

Representations through more general functions

Through Meijer G

Through other functions

Representations through equivalent functions

History

– Joh. Bernoulli (1702)
– H. Kühn (1753)
– L. Euler (1755) used the word "complex" (1777) and first used the letter i for (Sqrt[-1])
– H. D. Truel (1786)
– C. V. Mourey (1828)
– J. R. Argand (1806)
– C. F. Gauss (1831) introduced the name "imaginary unit"

The constant i is encountered often in mathematics and the natural sciences.

Copyright