1COMPLEX(7) complex math 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.
14 There are other ways to represent that number. The pair (a,b) of real
15 numbers may be viewed as a point in the plane, given by X- and Y-coor‐
16 dinates. This same point may also be described by giving the pair of
17 real numbers (r,phi), where r is the distance to the origin O, and phi
18 the angle between the X-axis and the line Oz. Now z = r*exp(i*phi) =
19 r*(cos(phi)+i*sin(phi)).
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21 The basic operations are defined on z = a+b*i and w = c+d*i as:
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23 addition: z+w = (a+c) + (b+d)*i
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25 multiplication: z*w = (a*c - b*d) + (a*d + b*c)*i
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27 division: z/w = ((a*c + b*d)/(c*c + d*d)) + ((b*c - a*d)/(c*c + d*d))*i
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29 Nearly all math function have a complex counterpart but there are some
30 complex only functions.
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33 Your C-compiler can work with complex numbers if it supports the C99
34 standard. Link with -lm. The imaginary unit is represented by I.
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36 /* check that exp(i*pi) == -1 */
37 #include <math.h> /* for atan */
38 #include <complex.h>
39 main() {
40 double pi = 4*atan(1);
41 complex z = cexp(I*pi);
42 printf("%f+%f*i\n", creal(z), cimag(z));
43 }
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46 cabs(3), carg(3), cexp(3), cimag(3), creal(3)
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50 2002-07-28 COMPLEX(7)