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COMPLEX(7)			    Linux Programmer's Manual			       COMPLEX(7)

       complex - basics of complex mathematics

       #include <complex.h>

       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) =

       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  func-

       Your  C-compiler can work with complex numbers if it supports the C99 standard.	Link with
       -lm.  The imaginary unit is represented by I.

       /* check that exp(i * pi) == -1 */
       #include <math.h>	/* for atan */
       #include <stdio.h>
       #include <complex.h>

	   double pi = 4 * atan(1.0);
	   double complex z = cexp(I * pi);
	   printf("%f + %f * i\n", creal(z), cimag(z));

       cabs(3), cacos(3), cacosh(3), carg(3), casin(3), casinh(3), catan(3), catanh(3),  ccos(3),
       ccosh(3),  cerf(3),  cexp(3),  cexp2(3),  cimag(3), clog(3), clog10(3), clog2(3), conj(3),
       cpow(3), cproj(3), creal(3), csin(3), csinh(3), csqrt(3), ctan(3), ctanh(3)

       This page is part of release 3.53 of the Linux man-pages project.  A  description  of  the
       project,     and    information	  about    reporting	bugs,	 can	be    found    at

					    2011-09-16				       COMPLEX(7)
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