|Definition:|| element of a set containing the real numbers and other elements, which may be represented by an ordered pair of real numbers (a, b), with following properties: |
- the pair (a, 0) represents the real number a,
- an addition is defined by ,
- a multiplication is defined by
Note 1 to entry: All properties of real numbers (operations and limits) are extended to complex numbers except the order relation.
Note 2 to entry: The complex number defined by the pair (a, b) is denoted by where j is the imaginary unit (IEV 102-02-10) represented by the pair (0, 1), a is the real part and b the imaginary part. A complex number may also be expressed as where is a non-negative real number called modulus and φ a real number called argument.
Note 3 to entry: In electrotechnology, a complex number is usually denoted by an underlined letter symbol, for example .
Note 4 to entry: The set of complex numbers is denoted by ℂ (C with a vertical bar in the left arc) or C. This set without zero is denoted by an asterisk to the symbol, for example ℂ*.