COMPLEX
Section: Linux Programmer's Manual (7)
Updated: 20200609
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NAME
complex  basics of complex mathematics
SYNOPSIS
#include <complex.h>
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
Ycoordinates.
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 Xaxis 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 complexonly functions.
EXAMPLES
Your Ccompiler 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>
int
main(void)
{
double pi = 4 * atan(1.0);
double complex z = cexp(I * pi);
printf("%f + %f * i\n", creal(z), cimag(z));
}
SEE ALSO
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)
COLOPHON
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