#pragma once
#include <vector>
#include <ostream>

//a*x^n
struct Term{
    double a;
    unsigned n;

    Term(double a, int n);
};

//a+bi
struct Complex{
    double a, b;
    Complex(double a, double b);
    Complex(double a);
    Complex();
};

Complex operator + (Complex A, Complex B);
Complex operator - (Complex A, Complex B);
Complex operator * (Complex A, Complex B);
Complex operator / (Complex A, Complex B);
bool operator == (Complex A, Complex B);

Complex pow(Complex c, int n);

std::ostream& operator << (std::ostream& out, Complex c);

//temporary construct for the actual solving.
struct Polynomial{
    std::vector<Term> p;

    Complex eval(Complex x);
    int degree();
    std::vector<Complex> solve();
};

std::ostream& operator << (std::ostream& out, Polynomial p);