http://blogs.msdn.com/b/vcblog/archive/2013/07/19/c99-library-support-in-visual-studio-2013.aspx

El soporte C99 agregó Visual Studio 2013, pero no puedo usar complex.h en mi código "C".

#include <stdio.h>
#include <complex.h>
int main(void)
{
    double complex dc1 = 3 + 2 * I;
    double complex dc2 = 4 + 5 * I;
    double complex result;

    result = dc1 + dc2;
    printf(" ??? \n", result);

    return 0;
}

Recibo errores de sintaxis.

Editar: Perdón por la parte que falta.

error C2146: syntax error : missing ';' before identifier 'dc1'
error C2065: 'dc1' : undeclared identifier
error C2088: '*' : illegal for struct
error C2086: 'double complex' : redefinition
error C2146: syntax error : missing ';' before identifier 'dc2'
error C2065: 'dc2' : undeclared identifier
error C2088: '*' : illegal for struct
error C2086: 'double complex' : redefinition
error C2146: syntax error : missing ';' before identifier 'result'
error C2065: 'result' : undeclared identifier
error C2065: 'result' : undeclared identifier
error C2065: 'dc1' : undeclared identifier
error C2065: 'dc2' : undeclared identifier
error C2065: 'result' : undeclared identifier           
IntelliSense: expected a ';'
IntelliSense: expected a ';'
IntelliSense: expected a ';'
IntelliSense: identifier "result" is undefined
IntelliSense: identifier "dc1" is undefined
IntelliSense: identifier "dc2" is undefined