work_w/_complex_numbers

#include <iostream> //exercise 16
#include <vector> //realize functions for complex numbers: input&output in algebraic and trigonometric form,
#include <math.h> //determination of modulus and argument of number, addition, subtraction, multiplication and division of complex numbers, involution

#define PI 3.14159265 //a + bi == re + im * i

using namespace std;

struct complex
{
    complex();
    double re; //real part of complex number
    double im; //imaginary part
    double r; //modulus
    double u; //the angle between the representing number vector and the positive direction of the Ox(argument)
    complex(double re, double im, double r, double u) : re(re), im(im), r(r), u(u) {};
};

vector<complex> c;

void printAlg(complex c)
{
    cout.setf(ios::showpos);//explicit sign identification
    cout << c.re << c.im << "i\n";
}

void printTrig(complex c)
{
    cout << c.r << "(cos(" << c.u * 180 / PI << " dgr) + sin(" << c.u * 180 / PI << " dgr)i)\n";//degree-form makes human perception much easier, i think
}

void modArg(complex& c)//modulus and argument
{
    c.r = sqrt(c.re * c.re + c.im * c.im);
    if (c.re == 0)
    {
        if (c.im >= 0)
            c.u = PI / 2;
        else
            c.u = PI * 3 / 2;
    }
    else
    {
        double ccos = c.re / c.r;
        if (ccos >= 0)
            c.u = atan(c.im / c.re);
        else
            c.u = PI + atan(c.im / c.re);
    }
}

void algForm(complex& c)
{
    c.re = c.r * cos(c.u);
    c.im = c.r * sin(c.u);
}


void input()
{
    bool inputForm;
    cout << "If you want to input comlex number in algebraic form, press 1;\nIf in trigonometric, press 0.\n";
    cin >> inputForm;
    if (inputForm)
    {
        cout << "Algebraic form: a + bi. Enter a and b.\n";
        double a, b;
        cin >> a >> b;
        c.push_back(complex(a, b, 0, 0));
        modArg(c.back());
    }
    else
    {
        cout << "Trigonometric form: r(cos u + sin u. Enter r and u(an angle should be expressed in degrees).\n";
        double r, u;
        cin >> r >> u;
        u = u * PI / 180; //trigonometric functions work with radian-format
        c.push_back(complex(0, 0, r, u));
        algForm(c.back());
    }
}

void addition(complex a, complex b)//+
{
    c.push_back(complex(a.re + b.re, a.im + b.im, 0, 0));
    modArg(c.back());
    cout << "\nAddition\n";
    printAlg(c.back());
    printTrig(c.back());
}

void subtraction(complex a, complex b)//-
{
    c.push_back(complex(a.re - b.re, a.im - b.im, 0, 0));
    modArg(c.back());
    cout << "\nSubtraction\n";
    printAlg(c.back());
    printTrig(c.back());
}

void multiplication(complex a, complex b)//*
{
    c.push_back(complex(a.re * b.re - a.im * b.im, a.im * b.re + a.re * b.im, 0, 0));
    modArg(c.back());
    cout << "\nMultiplication\n";
    printAlg(c.back());
    printTrig(c.back());
}

void division(complex a, complex b)//:
{
    c.push_back(complex((a.re * b.re + a.im * b.im) / (b.re * b.re + b.im * b.im), (a.im * b.re - a.re * b.im) / (b.re * b.re + b.im * b.im), 0, 0));
    modArg(c.back());
    cout << "\nDivision\n";
    printAlg(c.back());
    printTrig(c.back());
}

void involution(complex a)//a^x
{
    cout << "\nFor involution enter the degree number: ";
    int n;
    cin >> n;
    double r = 1;
    for(int i = 0; i < n; i++)
        r *= a.r;
    c.push_back(complex(0, 0, r, n * a.u));
    cout << "\nInvolution\n";
    printTrig(c.back());
}

int main()
{
    cout << "For some operations we need to take 2 complex numbers, so you should enter 2 complex numbers.\n";
    input();
    input();
    addition(c[0], c[1]);
    subtraction(c[0], c[1]);
    multiplication(c[0], c[1]);
    cout << "\nDevide the first number be the second.";
    division(c[0], c[1]);
    cout << "\nInvolution the first number.";
    involution(c[0]);

    system("pause");
    return 0;
}