mirror of https://github.com/mkerrisk/man-pages
50 lines
1.5 KiB
Groff
50 lines
1.5 KiB
Groff
.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
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.\" Distributed under GPL
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.\"
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.TH COMPLEX 7 2002-07-28 "" "complex math"
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.SH NAME
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complex \- basics of complex mathematics
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.SH SYNOPSIS
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.B #include <complex.h>
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.SH DESCRIPTION
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Complex numbers are numbers of the form z = a+b*i, where a and b are
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real numbers and i = sqrt(\-1), so that i*i = \-1.
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.br
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There are other ways to represent that number. The pair (a,b) of real
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numbers may be viewed as a point in the plane, given by X- and
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Y-coordinates. This same point may also be described by giving
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the pair of real numbers (r,phi), where r is the distance to the origin O,
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and phi the angle between the X-axis and the line Oz. Now
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z = r*exp(i*phi) = r*(cos(phi)+i*sin(phi)).
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.PP
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The basic operations are defined on z = a+b*i and w = c+d*i as:
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.TP
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.B addition: z+w = (a+c) + (b+d)*i
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.TP
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.B multiplication: z*w = (a*c \- b*d) + (a*d + b*c)*i
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.TP
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.B division: z/w = ((a*c + b*d)/(c*c + d*d)) + ((b*c \- a*d)/(c*c + d*d))*i
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.PP
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Nearly all math function have a complex counterpart but there are
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some complex only functions.
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.SH EXAMPLE
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Your C-compiler can work with complex numbers if it supports the C99 standard.
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Link with \-lm. The imaginary unit is represented by I.
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.sp
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.nf
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/* check that exp(i*pi) == \-1 */
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#include <math.h> /* for atan */
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#include <complex.h>
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main() {
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double pi = 4*atan(1);
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complex z = cexp(I*pi);
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printf("%f+%f*i\\n", creal(z), cimag(z));
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}
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.fi
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.SH "SEE ALSO"
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.BR cabs (3),
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.BR carg (3),
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.BR cexp (3),
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.BR cimag (3),
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.BR creal (3)
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