COMPLEX(3)               BSD Library Functions Manual               COMPLEX(3)

NAME
     complex -- complex floating-point functions

SYNOPSIS
     #include <complex.h>

DESCRIPTION
     The header file complex.h provides function prototypes and macros for
     working with complex floating-point values.  The functions conform to the
     ISO/IEC 9899:2011 standard.  In particular, arguments with infinite real
     or imaginary parts are regarded as infinities, even if the other part is
     a NaN.

     complex.h defines the macro complex for use as a type specifier, and the
     macro I to be the imaginary unit, which can be used to construct complex
     floating-point numbers from two real floating-point numbers.  For exam-
     ple:

           #include <complex.h>
           double complex z = 1.0 + 1.0 * I;  // z = 1 + i

     Note however that certain complex values cannot be initialized using this
     technique, because I is actually a complex value.  For example:

           double complex z = 0.0 + INFINITY * I;

     does not produce the result that one might expect; because of the promo-
     tion rules, it is evaluated like this:

           0.0 + INFINITY * I = 0.0 + inf*(0.0,1.0)
                              = 0.0 + (inf,0.0)*(0.0,1.0)
                              = 0.0 + (inf*0.0 - 1.0*0.0, inf*1.0 + 0.0*0.0)
                              = 0.0 + (NaN - 0.0, inf + 0.0)
                              = 0.0 + (NaN, inf)
                              = (0.0, 0.0) + (NaN, inf)
                              = (0.0 + NaN, 0.0 + inf)
                              = (NaN, inf)

     For this reason, and to allow the initialization of complex objects with
     static or thread storage duration, C11 introduced the following macros:

     double complex CMPLX(double x, double y)
     float complex CMPLXF(float x, float y)
     long double complex CMPLXL(long double x, long double y)

     These produce a complex number with real part having the converted value
     x and imaginary part y.

     Each of the functions that use complex floating-point values are provided
     in single, double, and extended precision; the double precision proto-
     types are listed here.  The man pages for the individual functions pro-
     vide more details on their use, special cases, and prototypes for their
     single and extended precision versions.

     The double-precision functions defined in complex.h are:

     double creal(double complex z)
     double cimag(double complex z)

     creal() and cimag() take a complex floating-point number and return its
     real and imaginary part, respectively, as real floating-point numbers.

     double cabs(double complex z)
     double carg(double complex z)

     cabs() and 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 coordi-
     nates, and are fully specified in terms of real functions:

           cabs(x + iy) = hypot(x,y)
           carg(x + iy) = atan2(y,x)

     double complex conj(double complex z)

     conj() takes a complex floating-point number and returns its complex con-
     jugate.

     double complex cproj(double complex z)

     cproj() takes a complex floating-point number and returns its projection
     onto the Riemann sphere, as defined in the C standard.  For non-infinite
     inputs, the return value is equal to the input value.

     double complex csqrt(double complex z)

     csqrt() takes a complex floating-point number and returns its square
     root, with a branch cut on the negative real axis.

     double complex cexp(double complex z)
     double complex clog(double complex z)

     cexp() and clog() take a complex floating-point number and return its
     base-e exponential and logarithm, respectively.  clog() has a branch cut
     on the negative real axis.

     double complex cpow(double complex z, double complex w)

     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 param-
     eter along the negative real axis.

     double complex csin(double complex z)
     double complex ccos(double complex z)
     double complex ctan(double complex z)

     csin(), ccos(), and ctan() take a complex floating-point number and
     return its sine, cosine, and tangent, respectively.

     double complex casin(double complex z)
     double complex cacos(double complex z)
     double complex catan(double complex z)

     casin(), cacos(), and catan() take a complex floating-point number and
     return its inverse sine, cosine, and tangent, respectively.

     casin() and cacos() have branch cuts outside the interval [-1, 1] on the
     real axis, and catan() has a branch cut outside the interval [-i, i] on
     the imaginary axis.

     double complex csinh(double complex z)
     double complex ccosh(double complex z)
     double complex ctanh(double complex z)

     csinh(), ccosh(), and ctanh() take a complex floating-point number and
     return its hyperbolic sine, cosine, and tangent, respectively.

     double complex casinh(double complex z)
     double complex cacosh(double complex z)
     double complex catanh(double complex z)

     casinh(), cacosh(), and catanh() take a complex floating-point number and
     return its inverse hyperbolic sine, cosine, and tangent, respectively.

     casinh() has a branch cut outside the interval [-i, i] on the imaginary
     axis.  cacosh() has a branch cut at values less than 1 on the real axis.
     catanh() has a branch cut outside the interval [-1, 1] on the real axis.

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.

SEE ALSO
     cabs(3), cacos(3), cacosh(3), carg(3), casin(3), casinh(3), catan(3),
     catanh(3), ccos(3), ccosh(3), cexp(3), cimag(3), clog(3), conj(3),
     cpow(3), cproj(3), creal(3), csin(3), csinh(3), csqrt(3), ctan(3),
     ctanh(3), math(3)

STANDARDS
     The <complex.h> functions conform to ISO/IEC 9899:2011.

BSD                             August 16, 2012                            BSD