015a_complex.asciidoc

cacos

NAME

cacos - complex arc cosine

SYNOPSIS

#include <complex.h>

#define imaginary _Imaginary
#define complex   _Complex

#define Imaginary_I
#define _Complex_I
#define I

#define CMPLX(x, y) ((double complex)((double)(x) + \
                    _Imaginary_I * (double) (y)))
#define CMPLXF(x, y) ((float complex)((float)(x) + \
                    _Imaginary_I * (float) (y)))
#define CMPLXL(x, y) ((long double complex)((long double)(x) + \
                    _Imaginary_I * (long double) (y)))

CONFORMING TO

C11

DESCRIPTION

Complex numbers are numbers of the form z = a+b*I, where a and b are real numbers and I = sqrt(-1), so that I*I = -1.

There are other ways to represent that number.The pair (a,b) of real numbers may be viewed as a point in the plane, given by X- and Y-coordinates. This same point may also be described by giving the pair of real numbers (r,phi), where r is the distance to the origin O, and phi the angle between the X-axis and the line Oz. Now z = r*exp(I*phi) = r*(cos(phi)+I*sin(phi)).

The basic operations are defined on z = a+b*I and w = c+d*I as:

addition: z+w = (a+c) + (b+d)*I

multiplication: z*w = (a*c - b*d) + (a*d + b*c)*I

division: z/w = a*c + b*d)/(c*c + d*d + b*c - a*d)/(c*c + d*d*I

Nearly all math function have a complex counterpart but there are some complex-only functions.

The macros CMPLX return a complex number composed of real as the real part and imag as the imaginary part.

The returned value is suitable for use as an initializer for variables with static or thread storage duration, but only if real and imag are also suitable.

RETURN VALUE

A complex number composed of real and imag as the real and imaginary parts.

SEE ALSO

complex

EXAMPLE

link:src/complex1.c[role=include]

OUTPUT

$ gcc -Wall -lm complex1.c
$ ./a.out
__STDC_NO_COMPLEX__ is undefined.
__STDC_IEC_559_COMPLEX__ is defined.
I = 0.0+1.0i
sizeof(I) = 8
sizeof(_Complex_I) = 8
z = 1.0+2.0i

EXAMPLE

link:src/complex2.c[role=include]

OUTPUT

$ gcc -Wall -lm complex2.c
$ ./a.out
-1.000000 + 0.000000 * i