#include <complex.h>

#ifdef __cplusplus
extern "C" {
#endif

...

/*** libiir++.cpp ***/
// we need to include "iir.h" first, as it pulls in <complex.h>, which we need
// to take effect before "iir++.h" pulls in <complex>
#include "iir.h"

// now remove the preprocessor definition of complex to _Complex, which is fine
// for the C header but not good for the C++ header
#undef complex

#include "iir++.h"

namespace IIR {

...

/*** iir++.h ***/
#include <complex>

namespace IIR {

...

./iir.h:570:15: error: expected ';' after top level declarator
double complex iir_response_c(const struct iir_coeff_t* coeff, double freq);
              ^
              ;