Manpages - complex.7

complex - basics of complex mathematics

  #include <complex.h>

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)*i

multiplication: z*w = (a*c - b*d) + (a*d + b*c)*i

(no term)

division: z/w = ((a*c + b*d)/(c*c + d*d)) + ((b*c - a*d)/(c*c + d*d))*i ::

Nearly all math function have a complex counterpart but there are some complex-only functions.

Your C-compiler can work with complex numbers if 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 <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));
  }

*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)

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