ぺんぎんさんからの練習問題 https://twitter.com/penguin2716/status/343915935712825346

complex.cpp

#include <iostream>
#include <cmath>

template<typename T> struct complex
{
    T real,imag;
    complex(T arg1,T arg2) : real(arg1),imag(arg2)
	{
	}
    complex(T arg) : real(arg),imag(0)
	{
	}
    template<typename N=double> N abs() const
	{
	    return std::sqrt(std::pow(this->real,2) + std::pow(this->imag,2));
	}
    bool operator==(complex<T> arg) const
	{
	    return this->real==arg.real and this->imag==arg.imag;
	}
    complex<T> conj() const
	{
	    return complex(this->real, this->imag * -1);
	}
    complex<T> operator+(const complex a) const
	{
	    return complex(this->real + a.real,this->imag + a.imag);   
	}
    complex<T> operator-(const complex a) const
	{
	    return complex(this->real - a.real,this->imag + a.imag);
	}
    complex<T> operator*(const complex a) const
	{
	    return complex(this->real * a.real + this->imag * a.imag ,
			   this->imag * a.real + this->real * a.imag);
	}
    complex<T> operator/(const complex a) const
	{
	    return complex((this->real * a.real + this->imag * a.imag)
			   / (std::pow(a.real,2) + std::pow(a.imag,2)),
			   (this->imag * a.real + this->real * a.imag)
			   / (std::pow(a.real,2) + std::pow(a.imag,2)));
	}
}
    ;
template<typename T>
std::ostream& operator<<(std::ostream& os, const complex<T>& c)
{
    return (c.imag==0)? (os << c.real):
	(c.imag<0)? (os << c.real << c.imag << 'i') :
	(os << c.real << '+' << c.imag << 'i');
}
int main()
{
    auto hoge = complex<double>(3,4);
    
    std::cout << hoge << std::endl;
    std::cout << hoge.abs() << std::endl;
    std::cout << hoge * 2 << std::endl;
    std::cout << hoge - 3 << std::endl;
    
}