complex.h

complex.h is a header file in the standard library of the C programming language that defines functionality for complex arithmetic.^[1] These functions use the built-in type complex which was introduced with the C99 revision of C.

This header should not be confused with the C++ standard library header <complex>, which implements complex numbers in a completely different way (as a template class, complex<T>).

Macro

Universal macro:

• complex - alias of _Complex
• _Complex_I - constant, which has type "const float _Complex" and value of imaginary unit I, I*I=-1

Defined only for `C99 Annex G`-compatible compiler modes - native support of imaginary types (it is very rare because Annex G is mathematically incorrect^[2]):

• imaginary - alias of _Imaginary
• _Imaginary_I Expands to a constant expression of type const float _Imaginary with the value of the imaginary unit.

Universal alias of I:

• I - alias of _Imaginary_I if it is defined else - alias of _Complex_I

Application may undefine complex, imaginary, and I macros if they interfere with internal values.

Functions

Each function declared in complex.h has three versions, each of which works with a different floating-point type (double, float and long double). Only the double version of each function is listed here; to use the float (or long double) version, append an f (or an l, respectively) to the function's name.

Note that all angles are in radians.

double         cabs(double complex);	Absolute value
double complex cacos(double complex);	Complex inverse cosine
double complex cacosh(double complex);	Complex inverse hyperbolic cosine
double         carg(double complex);	Complex argument
double complex casin(double complex);	Complex inverse sine
double complex casinh(double complex);	Complex inverse hyperbolic sine
double complex catan(double complex);	Complex inverse tangent
double complex catanh(double complex);	Complex inverse hyperbolic tangent
double complex ccos(double complex);	Complex cosine
double complex ccosh(double complex);	Complex hyperbolic cosine
double complex cexp(double complex);	Complex exponential
double         cimag(double complex);	Imaginary part of complex number
double complex clog(double complex);	Complex logarithm
double complex conj(double complex);	Complex conjugate
double complex cpow(double complex, double complex);	Complex power
double complex cproj(double complex);	Complex projection[A]
double         creal(double complex);	Real part of complex number
double complex csin(double complex);	Complex sine
double complex csinh(double complex);	Complex hyperbolic sine
double complex csqrt(double complex);	Complex square root
double complex ctan(double complex);	Complex tangent
double complex ctanh(double complex);	Complex hyperbolic tangent

^A cproj(z) projects the complex number z onto the Riemann sphere; the result is z itself, except complex infinities are mapped to positive infinity on the real axis.^[3]

References

1. complex.h: complex arithmetic – Base Definitions Reference, The Single UNIX Specification, Version 5 from The Open Group
2. Dr. Dobb's journal: software tools for the professional programmer, Volume 27 "many results in Annex G are pure invention and mathematically incorrect"
3. cproj: complex projection function – System Interfaces Reference, The Single UNIX Specification, Version 5 from The Open Group