mirror of https://github.com/mkerrisk/man-pages
84 lines
1.9 KiB
Groff
84 lines
1.9 KiB
Groff
.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
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.\"
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.\" %%%LICENSE_START(GPL_NOVERSION_ONELINE)
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.\" Distributed under GPL
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.\" %%%LICENSE_END
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.\"
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.TH COMPLEX 7 2021-03-22 "" "Linux Programmer's Manual"
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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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.nf
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.B #include <complex.h>
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.fi
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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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.PP
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There are other ways to represent that number.
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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.
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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.
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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 EXAMPLES
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Your C-compiler can work with complex numbers if it supports the C99 standard.
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Link with \fI\-lm\fP.
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The imaginary unit is represented by I.
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.PP
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.EX
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/* check that exp(i * pi) == \-1 */
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#include <math.h> /* for atan */
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#include <stdio.h>
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#include <complex.h>
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int
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main(void)
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{
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double pi = 4 * atan(1.0);
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double complex z = cexp(I * pi);
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printf("%f + %f * i\en", creal(z), cimag(z));
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}
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.EE
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.SH SEE ALSO
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.BR cabs (3),
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.BR cacos (3),
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.BR cacosh (3),
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.BR carg (3),
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.BR casin (3),
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.BR casinh (3),
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.BR catan (3),
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.BR catanh (3),
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.BR ccos (3),
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.BR ccosh (3),
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.BR cerf (3),
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.BR cexp (3),
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.BR cexp2 (3),
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.BR cimag (3),
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.BR clog (3),
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.BR clog10 (3),
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.BR clog2 (3),
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.BR conj (3),
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.BR cpow (3),
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.BR cproj (3),
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.BR creal (3),
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.BR csin (3),
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.BR csinh (3),
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.BR csqrt (3),
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.BR ctan (3),
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.BR ctanh (3)
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