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**NAME**

complex - basics of complex mathematics

**LIBRARY**

Math library (libm,-lm)

**SYNOPSIS**

#include<complex.h>

**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. 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)). 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.

**EXAMPLES**

Your C-compiler can work with complex numbers if it supports the C99 standard. The imaginary unit is represented by I. /* check that exp(i * pi) == -1 */ #include <math.h> /* for atan */ #include <stdio.h> #include <complex.h> int main(void) { double pi = 4 * atan(1.0); double complex z = cexp(I * pi); printf("%f + %f * i\n", creal(z), cimag(z)); }

**SEE** **ALSO**

cabs(3),cacos(3),cacosh(3),carg(3),casin(3),casinh(3),catan(3),catanh(3),ccos(3),ccosh(3),cerf(3),cexp(3),cexp2(3),cimag(3),clog(3),clog10(3),clog2(3),conj(3),cpow(3),cproj(3),creal(3),csin(3),csinh(3),csqrt(3),ctan(3),ctanh(3)