#include <iostream>
#include <cmath>
#include <cassert>
#include "Complex.h"

Complex rootN(const Complex& z, int n) {
    assert(n > 0);
    double magnitude = pow(abs(z), 1./double(n));
    double angle = arg(z)/double(n);
    return polar(magnitude, angle);
} 

Complex unitRootN(int n) {
    assert(n > 0);
    double angle = 2.*M_PI/double(n);
    return polar(1., angle);
}