#include <complex.h>
#include <stdio.h>
#include <math.h>

#ifndef J
#define J _Imaginary_I
#endif

int main();

int main() {
	int i, j;

	char *ordinals[14] = {
		"zeroeth", "first",    "second",   "third",     "fourth", 
		"fifth",   "sixth",    "seventh",  "eighth",    "nineth", 
		"tenth",   "eleventh", "twelveth", "thirteenth"
	};

	for ( i = 1; i <= 13; ++i ) {
		double const PI = acos( -1.0 );
		double complex z, w;

		printf( "The %s roots of unity:\n", ordinals[i] );

		// The principal ith root of unity
		//   - must compile with the -std=c11 option
		z = CMPLX( cos(2.0*PI/i), sin(2.0*PI/i) );

		// If only C99 is available, use this instead:
		// z = cos(2.0*PI/i) + sin(2.0*PI/i)*J;

		for ( j = 1; j <= i; ++j ) {
			w = cpow( z, j );
			printf( "    %f%+fj\n", crealf(w), cimagf(w) );
		}

		printf( "\n" );
	}

	return 0;
}