The complex numbers are the field of numbers of
the form , where and are real
numbers and * i * is the imaginary
unit equal to the square root of , . When a
single letter is used to denote a complex number,
it is sometimes called an " affix ." In component
notation, can be written . The field
of complex numbers includes the field of real
numbers as a subfield .

The set of complex numbers is implemented in the Wolfram Language as Complexes .
A number can then be tested to see if it is complex
using the command Element [* x* ,
Complexes ],
and expressions that are complex numbers have the Head
of Complex .

Complex numbers are useful abstract quantities that can be used in calculations and result in physically meaningful solutions. However, recognition of this fact is one that took a long time for mathematicians to accept. For example, John Wallis wrote, "These Imaginary Quantities (as they are commonly called) arising from the Supposed Root of a Negative Square (when they happen) are reputed to imply that the Case proposed is Impossible" (Wells 1986, p. 22).

The C programming language, as of C99, supports complex number math with the three built-in types double _Complex , float _Complex , and long double _Complex (see _Complex ). When the header <complex.h> is included, the three complex number types are also accessible as double complex , float complex , long double complex .

In addition to the complex types, the three imaginary types may be supported: double _Imaginary , float _Imaginary , and long double _Imaginary (see _Imaginary ). When the header <complex.h> is included, the three imaginary types are also accessible as double imaginary , float imaginary , and long double imaginary .

Standard arithmetic operators + , - , * , / can be used with real, complex, and imaginary types in any combination.

The complex numbers are the field of numbers of
the form , where and are real
numbers and * i * is the imaginary
unit equal to the square root of , . When a
single letter is used to denote a complex number,
it is sometimes called an " affix ." In component
notation, can be written . The field
of complex numbers includes the field of real
numbers as a subfield .

The set of complex numbers is implemented in the Wolfram Language as Complexes .
A number can then be tested to see if it is complex
using the command Element [* x* ,
Complexes ],
and expressions that are complex numbers have the Head
of Complex .

Complex numbers are useful abstract quantities that can be used in calculations and result in physically meaningful solutions. However, recognition of this fact is one that took a long time for mathematicians to accept. For example, John Wallis wrote, "These Imaginary Quantities (as they are commonly called) arising from the Supposed Root of a Negative Square (when they happen) are reputed to imply that the Case proposed is Impossible" (Wells 1986, p. 22).

The complex numbers are the field of numbers of
the form , where and are real
numbers and * i * is the imaginary
unit equal to the square root of , . When a
single letter is used to denote a complex number,
it is sometimes called an " affix ." In component
notation, can be written . The field
of complex numbers includes the field of real
numbers as a subfield .

The set of complex numbers is implemented in the Wolfram Language as Complexes .
A number can then be tested to see if it is complex
using the command Element [* x* ,
Complexes ],
and expressions that are complex numbers have the Head
of Complex .

Complex numbers are useful abstract quantities that can be used in calculations and result in physically meaningful solutions. However, recognition of this fact is one that took a long time for mathematicians to accept. For example, John Wallis wrote, "These Imaginary Quantities (as they are commonly called) arising from the Supposed Root of a Negative Square (when they happen) are reputed to imply that the Case proposed is Impossible" (Wells 1986, p. 22).

The C programming language, as of C99, supports complex number math with the three built-in types double _Complex , float _Complex , and long double _Complex (see _Complex ). When the header <complex.h> is included, the three complex number types are also accessible as double complex , float complex , long double complex .

In addition to the complex types, the three imaginary types may be supported: double _Imaginary , float _Imaginary , and long double _Imaginary (see _Imaginary ). When the header <complex.h> is included, the three imaginary types are also accessible as double imaginary , float imaginary , and long double imaginary .

Standard arithmetic operators + , - , * , / can be used with real, complex, and imaginary types in any combination.

The specializations std :: complex < float > , std :: complex < double > , and std :: complex < long double > are LiteralType s for representing and manipulating complex numbers .

For any object z of type complex<T> , reinterpret_cast < T ( & ) [ 2 ] > ( z ) [ 0 ] is the real part of z and reinterpret_cast < T ( & ) [ 2 ] > ( z ) [ 1 ] is the imaginary part of z.

For any pointer to an element of an array of complex<T> named p and any valid array index i , reinterpret_cast < T * > ( p ) [ 2 * i ] is the real part of the complex number p [ i ] , and reinterpret_cast < T * > ( p ) [ 2 * i + 1 ] is the imaginary part of the complex number p [ i ]

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