1COMPLEX(7) Linux Programmer's Manual COMPLEX(7)
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6 complex - basics of complex mathematics
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9 #include <complex.h>
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12 Complex numbers are numbers of the form z = a+b*i, where a and b are
13 real numbers and i = sqrt(-1), so that i*i = -1.
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15 There are other ways to represent that number. The pair (a,b) of real
16 numbers may be viewed as a point in the plane, given by X- and Y-coor‐
17 dinates. This same point may also be described by giving the pair of
18 real numbers (r,phi), where r is the distance to the origin O, and phi
19 the angle between the X-axis and the line Oz. Now z = r*exp(i*phi) =
20 r*(cos(phi)+i*sin(phi)).
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22 The basic operations are defined on z = a+b*i and w = c+d*i as:
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24 addition: z+w = (a+c) + (b+d)*i
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26 multiplication: z*w = (a*c - b*d) + (a*d + b*c)*i
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28 division: z/w = ((a*c + b*d)/(c*c + d*d)) + ((b*c - a*d)/(c*c + d*d))*i
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30 Nearly all math function have a complex counterpart but there are some
31 complex-only functions.
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34 Your C-compiler can work with complex numbers if it supports the C99
35 standard. Link with -lm. The imaginary unit is represented by I.
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37 /* check that exp(i * pi) == -1 */
38 #include <math.h> /* for atan */
39 #include <stdio.h>
40 #include <complex.h>
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42 int
43 main(void)
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45 double pi = 4 * atan(1.0);
46 double complex z = cexp(I * pi);
47 printf("%f + %f * i\n", creal(z), cimag(z));
48 }
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51 cabs(3), cacos(3), cacosh(3), carg(3), casin(3), casinh(3), catan(3),
52 catanh(3), ccos(3), ccosh(3), cerf(3), cexp(3), cexp2(3), cimag(3),
53 clog(3), clog10(3), clog2(3), conj(3), cpow(3), cproj(3), creal(3),
54 csin(3), csinh(3), csqrt(3), ctan(3), ctanh(3)
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57 This page is part of release 5.02 of the Linux man-pages project. A
58 description of the project, information about reporting bugs, and the
59 latest version of this page, can be found at
60 https://www.kernel.org/doc/man-pages/.
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64 2019-03-06 COMPLEX(7)