Complex number arithmetic
If the macro constant __STDC_NO_COMPLEX__ is defined by the implementation, the complex types, the header <complex.h> and all of the names listed here are not provided.
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.
A compiler that defines __STDC_IEC_559_COMPLEX__ is recommended, but not required to support imaginary numbers. POSIX recommends checking if the macro _Imaginary_I is defined to identify imaginary number support.
(until C11)
Imaginary numbers are supported if __STDC_IEC_559_COMPLEX__ or __STDC_IEC_60559_COMPLEX__(since C23) is defined.
<complex.h> Contents
Types
(keyword macro) [edit]
(keyword macro) [edit]
The imaginary constant
(macro constant) [edit]
(macro constant) [edit]
(macro constant) [edit]
Manipulation
(function macro) [edit]
(function) [edit]
(function) [edit]
(function) [edit]
(function) [edit]
(function) [edit]
(function) [edit]
Exponential functions
(function) [edit]
(function) [edit]
Power functions
(function) [edit]
(function) [edit]
Trigonometric functions
(function) [edit]
(function) [edit]
(function) [edit]
(function) [edit]
(function) [edit]
(function) [edit]
Hyperbolic functions
(function) [edit]
(function) [edit]
(function) [edit]
(function) [edit]
(function) [edit]
(function) [edit]
[edit] Notes
The following function names are potentially(since C23) reserved for future addition to <complex.h> and are not available for use in the programs that include that header: cerf, cerfc, cexp2, cexpm1, clog10, clog1p, clog2, clgamma, ctgamma, csinpi, ccospi, ctanpi, casinpi, cacospi, catanpi, ccompoundn, cpown, cpowr, crootn, crsqrt, cexp10m1, cexp10, cexp2m1, clog10p1, clog2p1, clogp1(since C23), along with their -f and -l suffixed variants.
Although the C standard names the inverse hyperbolic with "complex arc hyperbolic sine" etc., the inverse functions of the hyperbolic functions are the area functions. Their argument is the area of a hyperbolic sector, not an arc. The correct names are "complex inverse hyperbolic sine" etc. Some authors use "complex area hyperbolic sine" etc.
A complex or imaginary number is infinite if one of its parts is infinite, even if the other part is NaN.
A complex or imaginary number is finite if both parts are neither infinities nor NaNs.
A complex or imaginary number is a zero if both parts are positive or negative zeroes.
While MSVC does provide a <complex.h> header, it does not implement complex numbers as native types, but as structs, which are incompatible with standard C complex types and do not support the +, -, *, / operators.
[edit] Example
#include <complex.h> #include <stdio.h> #include <tgmath.h> int main(void) { double complex z1 = I * I; // imaginary unit squared printf ("I * I = %.1f%+.1fi\n", creal (z1), cimag (z1)); double complex z2 = pow (I, 2); // imaginary unit squared printf ("pow(I, 2) = %.1f%+.1fi\n", creal (z2), cimag (z2)); double PI = acos (-1); double complex z3 = exp (I * PI); // Euler's formula printf ("exp(I*PI) = %.1f%+.1fi\n", creal (z3), cimag (z3)); double complex z4 = 1 + 2 * I, z5 = 1 - 2 * I; // conjugates printf ("(1+2i)*(1-2i) = %.1f%+.1fi\n", creal (z4 * z5), cimag (z4 * z5)); }
Output:
I * I = -1.0+0.0i pow(I, 2) = -1.0+0.0i exp(I*PI) = -1.0+0.0i (1+2i)*(1-2i) = 5.0+0.0i
[edit] References
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