Программирование на С++.Комплексное число представляют парой действительных чисел (a,b).

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#include <iostream>
#include <string>
class Complex {
public:
constexpr Complex(const double& real = 0, const double& imag = 0) : real_(real), imag_(imag) { }
bool conj(const Complex& c)const {
int a = imag_ < 0 ? -1 : 0;
int b = c.imag_ < 0 ? -1 : 0;
return *this == c && a != b;
}
void read() {
std::cout << "a: ";
std::cin >> real_;
std::cout << "b: ";
std::cin >> imag_;
}
void display() {
std::cout << real_ << (imag_ < 0 ? " - " : " + ") << abs(imag_) << 'i';
}
std::string toString()const {
auto real = std::to_string(real_);
real.erase(real.find_last_not_of("0") + 1);
real.erase(real.find_last_not_of(".") + 1);
auto imag = std::to_string(abs(imag_));
imag.erase(imag.find_last_not_of("0") + 1);
imag.erase(imag.find_last_not_of(".") + 1);
return real + (imag_ < 0 ? " - " : " + ") + imag + "i";
}
private:
double real_;
double imag_;
friend Complex operator+(const Complex& a, const Complex& b) {
return Complex(a.real_ + b.real_, a.imag_ + b.imag_);
}
friend Complex operator-(const Complex& a, const Complex& b) {
return Complex(a.real_ - b.real_, a.imag_ - b.imag_);
}
friend Complex operator*(const Complex& a, const Complex& b) {
return Complex(a.real_ * b.real_ - a.imag_ * b.imag_, a.real_ * b.imag_ + b.real_ * a.imag_);
}
friend Complex operator/(const Complex& a, const Complex& b) {
auto aa = a.real_ * a.real_;
auto bb = a.imag_ * a.imag_;
auto ab = aa + bb;
if (a.conj(b)) return Complex(a.real_ / ab, -a.imag_ / ab);
auto cc = b.real_ * b.real_;
auto dd = b.imag_ * b.imag_;
auto ac = a.real_ * b.real_;
auto bd = a.imag_ * b.imag_;
auto bc = a.imag_ * b.real_;
auto ad = a.real_ * b.imag_;
auto cd = cc + dd;
return Complex((ac + bd) / cd, (bc - ad) / cd);
}
friend bool operator==(const Complex& a, const Complex& b) {
return a.real_ == b.real_ && a.imag_ == b.imag_;
}
};
int main() {
Complex x(7, 4);
x.display();
std::cout.put('\n');
Complex y(3, 2);
y.display();
std::cout.put('\n');
auto xy = x + y;
xy.display();
std::cout.put('\n');
auto yx = y + x;
yx.display();
std::cout.put('\n');
puts(xy == yx ? "Equal" : "Not equal");
auto sub = x - y;
sub.display();
std::cout.put('\n');
auto div = x / y;
div.display();
std::cout.put('\n');
auto mlt = x * y;
mlt.display();
std::cout.put('\n');
auto x_str = x.toString();
std::cout << x_str << '\n';
auto div_str = div.toString();
std::cout << div_str << '\n';
system("pause > nul");
}