1complex(7)             Miscellaneous Information Manual             complex(7)
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NAME

6       complex - basics of complex mathematics
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LIBRARY

9       Math library (libm, -lm)
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SYNOPSIS

12       #include <complex.h>
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DESCRIPTION

15       Complex  numbers  are  numbers of the form z = a+b*i, where a and b are
16       real numbers and i = sqrt(-1), so that i*i = -1.
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18       There are other ways to represent that number.  The pair (a,b) of  real
19       numbers  may be viewed as a point in the plane, given by X- and Y-coor‐
20       dinates.  This same point may also be described by giving the  pair  of
21       real  numbers (r,phi), where r is the distance to the origin O, and phi
22       the angle between the X-axis and the line Oz.  Now z =  r*exp(i*phi)  =
23       r*(cos(phi)+i*sin(phi)).
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25       The basic operations are defined on z = a+b*i and w = c+d*i as:
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27       addition: z+w = (a+c) + (b+d)*i
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29       multiplication: z*w = (a*c - b*d) + (a*d + b*c)*i
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31       division: z/w = ((a*c + b*d)/(c*c + d*d)) + ((b*c - a*d)/(c*c + d*d))*i
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33       Nearly  all math function have a complex counterpart but there are some
34       complex-only functions.
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EXAMPLES

37       Your C-compiler can work with complex numbers if it  supports  the  C99
38       standard.  The imaginary unit is represented by I.
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40       /* check that exp(i * pi) == -1 */
41       #include <math.h>        /* for atan */
42       #include <stdio.h>
43       #include <complex.h>
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45       int
46       main(void)
47       {
48           double pi = 4 * atan(1.0);
49           double complex z = cexp(I * pi);
50           printf("%f + %f * i\n", creal(z), cimag(z));
51       }
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SEE ALSO

54       cabs(3),  cacos(3),  cacosh(3), carg(3), casin(3), casinh(3), catan(3),
55       catanh(3), ccos(3), ccosh(3),  cerf(3),  cexp(3),  cexp2(3),  cimag(3),
56       clog(3),  clog10(3),  clog2(3),  conj(3),  cpow(3), cproj(3), creal(3),
57       csin(3), csinh(3), csqrt(3), ctan(3), ctanh(3)
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61Linux man-pages 6.05              2023-07-18                        complex(7)
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