complex.h man page
Prolog
This manual page is part of the POSIX Programmer's Manual. The Linux implementation of this interface may differ (consult the corresponding Linux manual page for details of Linux behavior), or the interface may not be implemented on Linux.
complex.h — complex arithmetic
Synopsis
#include <complex.h>
Description
The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of POSIX.1‐2008 defers to the ISO C standard.
The <complex.h> header shall define the following macros:
 complex
 Expands to _Complex.
 _Complex_I
 Expands to a constant expression of type const float _Complex, with the value of the imaginary unit (that is, a number i such that i^{2}=1).
 imaginary
 Expands to _Imaginary.
 _Imaginary_I
 Expands to a constant expression of type const float _Imaginary with the value of the imaginary unit.
 I
 Expands to either _Imaginary_I or _Complex_I. If _Imaginary_I is not defined, I expands to _Complex_I.
The macros imaginary and _Imaginary_I shall be defined if and only if the implementation supports imaginary types.
An application may undefine and then, perhaps, redefine the complex, imaginary, and I macros.
The following shall be declared as functions and may also be defined as macros. Function prototypes shall be provided.
double cabs(double complex);
float cabsf(float complex);
long double cabsl(long double complex);
double complex cacos(double complex);
float complex cacosf(float complex);
double complex cacosh(double complex);
float complex cacoshf(float complex);
long double complex cacoshl(long double complex);
long double complex cacosl(long double complex);
double carg(double complex);
float cargf(float complex);
long double cargl(long double complex);
double complex casin(double complex);
float complex casinf(float complex);
double complex casinh(double complex);
float complex casinhf(float complex);
long double complex casinhl(long double complex);
long double complex casinl(long double complex);
double complex catan(double complex);
float complex catanf(float complex);
double complex catanh(double complex);
float complex catanhf(float complex);
long double complex catanhl(long double complex);
long double complex catanl(long double complex);
double complex ccos(double complex);
float complex ccosf(float complex);
double complex ccosh(double complex);
float complex ccoshf(float complex);
long double complex ccoshl(long double complex);
long double complex ccosl(long double complex);
double complex cexp(double complex);
float complex cexpf(float complex);
long double complex cexpl(long double complex);
double cimag(double complex);
float cimagf(float complex);
long double cimagl(long double complex);
double complex clog(double complex);
float complex clogf(float complex);
long double complex clogl(long double complex);
double complex conj(double complex);
float complex conjf(float complex);
long double complex conjl(long double complex);
double complex cpow(double complex, double complex);
float complex cpowf(float complex, float complex);
long double complex cpowl(long double complex, long double complex);
double complex cproj(double complex);
float complex cprojf(float complex);
long double complex cprojl(long double complex);
double creal(double complex);
float crealf(float complex);
long double creall(long double complex);
double complex csin(double complex);
float complex csinf(float complex);
double complex csinh(double complex);
float complex csinhf(float complex);
long double complex csinhl(long double complex);
long double complex csinl(long double complex);
double complex csqrt(double complex);
float complex csqrtf(float complex);
long double complex csqrtl(long double complex);
double complex ctan(double complex);
float complex ctanf(float complex);
double complex ctanh(double complex);
float complex ctanhf(float complex);
long double complex ctanhl(long double complex);
long double complex ctanl(long double complex);
The following sections are informative.
Application Usage
Values are interpreted as radians, not degrees.
Rationale
The choice of I instead of i for the imaginary unit concedes to the widespread use of the identifier i for other purposes. The application can use a different identifier, say j, for the imaginary unit by following the inclusion of the <complex.h> header with:
#undef I
#define j _Imaginary_I
An I suffix to designate imaginary constants is not required, as multiplication by I provides a sufficiently convenient and more generally useful notation for imaginary terms. The corresponding real type for the imaginary unit is float, so that use of I for algorithmic or notational convenience will not result in widening types.
On systems with imaginary types, the application has the ability to control whether use of the macro I introduces an imaginary type, by explicitly defining I to be _Imaginary_I or _Complex_I. Disallowing imaginary types is useful for some applications intended to run on implementations without support for such types.
The macro _Imaginary_I provides a test for whether imaginary types are supported.
The cis() function (cos(x) + I*sin(x)) was considered but rejected because its implementation is easy and straightforward, even though some implementations could compute sine and cosine more efficiently in tandem.
Future Directions
The following function names and the same names suffixed with f or l are reserved for future use, and may be added to the declarations in the <complex.h> header.



See Also
The System Interfaces volume of POSIX.1‐2008, cabs(), cacos(), cacosh(), carg(), casin(), casinh(), catan(), catanh(), ccos(), ccosh(), cexp(), cimag(), clog(), conj(), cpow(), cproj(), creal(), csin(), csinh(), csqrt(), ctan(), ctanh()
Copyright
Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1, 2013 Edition, Standard for Information Technology  Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 7, Copyright (C) 2013 by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. (This is POSIX.12008 with the 2013 Technical Corrigendum 1 applied.) In the event of any discrepancy between this version and the original IEEE and The Open Group Standard, the original IEEE and The Open Group Standard is the referee document. The original Standard can be obtained online at http://www.unix.org/online.html .