我在ComplexNumber.cpp中的一些方法得到一个奇怪的未定义的错误引用，虽然[复制]我对模板很新

Question

这个问题在这里已有答案：

Why can templates only be implemented in the header file? 16个答案

得到c：/ mingw / bin /../ lib / gcc / mingw32 / 8.2.0 /../../../../ mingw32 / bin / ld.exe：main.o：main.cpp :( .text + 0x2b）：在运行G ++ main.o ComplexNumber.o -o输出后使用makefile进行编译时未定义的引用（在ComplexNumber.cpp中插入我的方法）。

我已经尝试在线查看我可能错过的地方，并使用我过去做过的其他头文件作为参考来检查那里的错误，但我没有运气。我在windows上使用cygdrive进行编译，但也尝试在常规命令提示符下使用mingw。

标题文件：'''''''''''

#include <stdio.h>


#ifndef COMPLEXNUMBER_H_
#define COMPLEXNUMBER_H_



template<typename T>

class ComplexNumber
{

    public:
        // a is a real number, b is a complex number
        T a;
        T b;
        ComplexNumber();
        ComplexNumber(T, T);
        void toString();
    ComplexNumber operator +(ComplexNumber<T>& c);
    ComplexNumber operator *(ComplexNumber<T>& c);
    bool operator ==(ComplexNumber<T>& c);
};



#endif /* COMPLEXNUMBER_H_ */

''''''''''''''

ComplexNumber.cpp''''''''''''

#include <iostream>
#include <stdlib.h>
#include <ctime>
#include "ComplexNumber.h"


using namespace std;


template <typename T>

    ComplexNumber<T>::ComplexNumber()
    {}
template <typename T>
ComplexNumber<T>::ComplexNumber(T a, T b)
{
    this->a = a;
    this->b = b;
}
template <typename T>
ComplexNumber<T> ComplexNumber<T>:: operator +(ComplexNumber& c)
{
    ComplexNumber <T> temp;

    // adds the complex numbers, (a+bi) + (c+di) = (a+b) + i(c+d)
    temp.a = this->a + c.a;
    temp.b = this->b + c.b;
    return temp;
}
template <typename T>
ComplexNumber<T> ComplexNumber<T>:: operator *(ComplexNumber& c)
{
    ComplexNumber<T> temp;

    // multiplies complex numbers, (a+bi) + (c+di) = (a*c-b*d) + i(a*d + b*c)
    temp.a = (this->a * c.a) - (temp.b * c.b);
    temp.b = (temp.a * c.b) + (temp.b * c.a);
    return temp;
}
template <typename T>
bool ComplexNumber<T>:: operator ==(ComplexNumber<T>& c)
{
    ComplexNumber<T> temp;

    // compares complex numbers to see if they're equal, (a+bi) == (c+di) -> if (a==c) & (b==d)
    if (temp.a == c.a && temp.b == c.b)
    {
        cout<< "The complex numbers are equal."<<endl;
        return true;
    }
    return false;
}
template <typename T>
void ComplexNumber<T>::toString()
{

    cout<< "("<< this->a<< " + "<< this->b<< "i)"<<endl;
}

MakeFile：''''''''''

all: ComplexNumber
ComplexNumber: main.o ComplexNumber.o
    g++ main.o ComplexNumber.o -o output
main.o: main.cpp
    g++ -c main.cpp
ComplexNumber.o: ComplexNumber.cpp
    g++ -c ComplexNumber.cpp
clean:
    rm *.o output

''''''''''''''