This is how you can use complex numbers from C. This code assumes that you have declared CCTK_COMPLEX grid functions u, v, w.

(I didn't actually try to compile this example, but the overall structure should be fine.)

#include <cctk.h>

#include <cctk_Arguments.h>

#include <complex.h>

#include <math.h>

void do_some_complex_calculations(CCTK_ARGUMENTS)

{

  DECLARE_CCTK_ARGUMENTS;

#pragma omp parallel for

  for (int k=0; k<cctk_lsh[2]; ++k) {

  for (int j=0; j<cctk_lsh[1]; ++j) {

  for (int i=0; i<cctk_lsh[0]; ++i) {

    const int idx = CCTK_GFINDEX3D(cctkGH, i,j,k);

    CCTK_COMPLEX tmp = 2.0 + 3.0 * I;

    u[idx] = conj(tmp) * v[idx] + 2.0 * cabs(w[idx]);

    u[idx] = cexp(u[idx]) - creal(tmp) + cimag(tmp);

  }

  }

  }

}