основы сложной математики (basics of complex mathematics)
Имя (Name)
complex - basics of complex mathematics
Синопсис (Synopsis)
#include <complex.h>
Описание (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.
Примеры (Examples)
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>
int
main(void)
{
double pi = 4 * atan(1.0);
double complex z = cexp(I * pi);
printf("%f + %f * i\n", creal(z), cimag(z));
}
Смотри также (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)
