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COMPLEX(5) complex math COMPLEX(5)NAMEcomplex - basics of complex mathematicsSYNOPSIS#include <complex.h>DESCRIPTIONComplex 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. There are other ways to represent that number. The pair (a,b) of real numbers may be viewed as a point in(1,8) the plane, given by X- and Y-coor- dinates. 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)). The basic operations are defined on z = a+b*i and w = c+d*i as:addition: z+w = (a+c) + (b+d)*imultiplication: z*w = (a*c - b*d) + (a*d + b*c)*idivision: z/w = ((a*c + b*d)/(c*c + d*d)) + ((b*c - a*d)/(c*c + d*d))*iNearly all math function have a complex counterpart but there are some complex only functions.EXAMPLEYour C-compiler can work with complex numbers if(3,n) it supports the C99 standard. Link with -lm. The imaginary unit is represented by I. /* 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(1,3,1 builtins)("%f+%f*i\n", creal(z), cimag(z)); }SEE ALSOcabs(3),carg(3),cexp(3),cimag(3),creal(3) 2002-07-28 COMPLEX(5)