.\" Copyright (c) 2006 Apple Computer .\" .Dd October 10, 2006 .Dt COMPLEX 3 .Os .Sh NAME .Nm complex .Nd complex floating-point functions .Sh SYNOPSIS .Fd #include <complex.h> .Sh DESCRIPTION The header file complex.h provides function prototypes and macros for working with C99 complex floating-point values. The functions conform to the ISO/IEC 9899:1999(E) standard. In particular, arguments with infinite real or imaginary parts are regarded as infinities, even if the other part is a NaN. .Pp complex.h defines the macro .Fa complex for use as a type specifier, and the macro .Fa I to be the imaginary unit, which can be used to construct complex floating-point numbers from two real floating-point numbers. For example: .Bd -literal -offset indent #include <complex.h> double complex z = 1.0 + 1.0 * I; // z = 1 + i .Ed .Pp Each of the functions that use complex floating-point values are provided in single, double, and extended precision; the double precision prototypes are listed here. The man pages for the individual functions provide more details on their use, special cases, and prototypes for their single and extended precision versions. .Pp The double-precision functions defined in complex.h are: .Pp .Ft double .Fn creal "double complex z" .Pp .Ft double .Fn cimag "double complex z" .Pp .Fn creal and .Fn cimag take a complex floating-point number and return its real and imaginary part, respectively, as real floating-point numbers. .Pp .Ft double .Fn cabs "double complex z" .Pp .Ft double .Fn carg "double complex z" .Pp .Fn cabs and .Fn carg take a complex floating-point number and return its norm and argument (phase angle), respectively, as real floating-point numbers. They are used to convert between rectangular and polar coordinates, and are fully specified in terms of real functions: .Bd -literal -offset indent cabs(x + iy) = hypot(x,y) .br carg(x + iy) = atan2(y,x) .Ed .Pp .Ft double complex .Fn conj "double complex z" .Pp .Fn conj takes a complex floating-point number and returns its complex conjugate. .Pp .Ft double complex .Fn cproj "double complex z" .Pp .Fn cproj takes a complex floating-point number and returns its projection onto the Riemann sphere, as defined in C99. For non-infinite inputs, the return value is equal to the input value. .Pp .Ft double complex .Fn csqrt "double complex z" .Pp .Fn csqrt takes a complex floating-point number and returns its square root, with a branch cut on the negative real axis. .Pp .Ft double complex .Fn cexp "double complex z" .Pp .Ft double complex .Fn clog "double complex z" .Pp .Fn cexp and .Fn clog take a complex floating-point number and return its base-e exponential and logarithm, respectively. .Fn clog has a branch cut on the negative real axis. .Pp .Ft double complex .Fn cpow "double complex z" "double complex w" .Pp .Fn cpow takes two complex floating-point numbers, and returns the first raised to the power of the second, with a branch cut for the first parameter along the negative real axis. .Pp .Ft double complex .Fn csin "double complex z" .Pp .Ft double complex .Fn ccos "double complex z" .Pp .Ft double complex .Fn ctan "double complex z" .Pp .Fn csin , .Fn ccos , and .Fn ctan take a complex floating-point number and return its sine, cosine, and tangent, respectively. .Pp .Ft double complex .Fn casin "double complex z" .Pp .Ft double complex .Fn cacos "double complex z" .Pp .Ft double complex .Fn catan "double complex z" .Pp .Fn casin , .Fn cacos , and .Fn catan take a complex floating-point number and return its inverse sine, cosine, and tangent, respectively. .Pp .Fn casin and .Fn cacos have branch cuts outside the interval .Bq -1, 1 on the real axis, and .Fn catan has a branch cut outside the interval .Bq -i, i on the imaginary axis. .Pp .Ft double complex .Fn csinh "double complex z" .Pp .Ft double complex .Fn ccosh "double complex z" .Pp .Ft double complex .Fn ctanh "double complex z" .Pp .Fn csinh , .Fn ccosh , and .Fn ctanh take a complex floating-point number and return its hyperbolic sine, cosine, and tangent, respectively. .Pp .Ft double complex .Fn casinh "double complex z" .Pp .Ft double complex .Fn cacosh "double complex z" .Pp .Ft double complex .Fn catanh "double complex z" .Pp .Fn casinh , .Fn cacosh , and .Fn catanh take a complex floating-point number and return its inverse hyperbolic sine, cosine, and tangent, respectively. .Pp .Fn casinh has a branch cut outside the interval .Bq -i, i on the imaginary axis. .Fn cacosh has a branch cut at values less than 1 on the real axis. .Fn catanh has a branch cut outside the interval .Bq -1, 1 on the real axis. .Sh NOTE Note that the complex math functions are not, in general, equivalent to their real counterparts for inputs on the real axis. For example, csqrt(-1 + 0i) is 0 + i, whereas sqrt(-1) is NaN. .Sh SEE ALSO .Xr cabs 3 , .Xr cacos 3 , .Xr cacosh 3 , .Xr carg 3 , .Xr casin 3 , .Xr casinh 3 , .Xr catan 3 , .Xr catanh 3 , .Xr ccos 3 , .Xr ccosh 3 , .Xr cexp 3 , .Xr cimag 3 , .Xr clog 3 , .Xr conj 3 , .Xr cpow 3 , .Xr cproj 3 , .Xr creal 3 , .Xr csin 3 , .Xr csinh 3 , .Xr csqrt 3 , .Xr ctan 3 , .Xr ctanh 3 , .Xr math 3 .Sh STANDARDS The <complex.h> functions conform to ISO/IEC 9899:1999(E).