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diff --git a/man5/complex.5 b/man5/complex.5 new file mode 100644 index 000000000..1347aded6 --- /dev/null +++ b/man5/complex.5 @@ -0,0 +1,49 @@ +.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de) +.\" Distributed under GPL +.\" +.TH COMPLEX 5 2002-07-28 "" "complex math" +.SH NAME +complex \- basics of complex mathematics +.SH SYNOPSIS +.B #include <complex.h> +.SH 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. +.br +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)). +.PP +The basic operations are defined on z = a+b*i and w = c+d*i as: +.TP +.B addition: z+w = (a+c) + (b+d)*i +.TP +.B multiplication: z*w = (a*c - b*d) + (a*d + b*c)*i +.TP +.B division: z/w = ((a*c + b*d)/(c*c + d*d)) + ((b*c - a*d)/(c*c + d*d))*i +.PP +Nearly all math function have a complex counterpart but there are +some complex only functions. +.SH EXAMPLE +Your C-compiler can work with complex numbers if it supports the C99 standard. +Link with -lm. The imaginary unit is represented by I. +.sp +.nf +/* check that exp(i*pi) == -1 */ +#include <math.h> /* for atan */ +#include <complex.h> +main() { + double pi = 4*atan(1); + complex z = cexp(I*pi); + printf("%f+%f*i\\n", creal(z), cimag(z)); +} +.fi +.SH "SEE ALSO" +.BR cabs (3), +.BR carg (3), +.BR cexp (3), +.BR cimag (3), +.BR creal (3) |