怎么用c++编写一个复数计算器？包括加减乘除、幂次方、取模、辐角、共轭。实部和虚部都是实数范围。

Question

比如（3.5+222i）^（-3）+0.12*arg（-2+5.1i）-｜33+4.667i｜/cjg（3-4i）=？
其中arg是辐角，cjg取共轭，｜｜是取模。实数范围内，需要用逆波兰。
不可以用c++自带的complex类，需要自己定义。
因初学这一部分，没有足够的练习，不太能上手这一类题目。希望可以给出较详细的代码，或者提供一个比较具体的思路指导。

Answer 1

部分引用GPT（有的实在是不会，没办法）
我帮你写一个：

#include <iostream>
#include <string>
#include <stack>
#include <cmath>

using namespace std;

class Complex {
public:
    double real;
    double imaginary;
    // 构造函数
    Complex(double real = 0, double imaginary = 0) {
        this->real = real;
        this->imaginary = imaginary;
    }
    // 重载运算符
    Complex operator + (const Complex& c) const {
        return Complex(real + c.real, imaginary + c.imaginary);
    }
    Complex operator - (const Complex& c) const {
        return Complex(real - c.real, imaginary - c.imaginary);
    }
    Complex operator * (const Complex& c) const {
        return Complex(real * c.real - imaginary * c.imaginary, real * c.imaginary + imaginary * c.real);
    }
    Complex operator / (const Complex& c) const {
        double denominator = c.real * c.real + c.imaginary * c.imaginary;
        return Complex((real * c.real + imaginary * c.imaginary) / denominator, (imaginary * c.real - real * c.imaginary) / denominator);
    }
    Complex operator ^ (int n) const {
        Complex result = *this;
        for (int i = 1; i < n; i++) {
            result = result * (*this);
        }
        return result;
    }
    double abs() const {
        return sqrt(real * real + imaginary * imaginary);
    }
    double arg() const {
        return atan2(imaginary, real);
    }
    Complex conjugate() const {
        return Complex(real, -imaginary);
    }
};

// 操作符优先级
int Priority(char op) {
    if (op == '+' || op == '-') {
        return 1;
    } else if (op == '*' || op == '/') {
        return 2;
    } else if (op == '^') {
        return 3;
    } else {
        return 0;
    }
}

// 四则运算
Complex Calculate(Complex a, Complex b, char op) {
    switch (op) {
    case '+':
        return a + b;
    case '-':
        return a - b;
    case '*':
        return a * b;
    case '/':
        return a / b;
    case '^':
        return a ^ (int)b.real;
    default:
        return Complex();
    }
}

// 逆波兰表达式求值
Complex Evaluate(const string& expression) {
    stack<char> opStack;
    stack<Complex> numStack;
    int index = 0;
    while (index < expression.length()) {
        if (isdigit(expression[index]) || expression[index] == '.') {
            double realPart = stod(expression.substr(index), &index);
            double imaginaryPart = 0;
            if (expression[index] == 'i') {
                index++;
                imaginaryPart = realPart;
                realPart = 0;
            }
            numStack.push(Complex(realPart, imaginaryPart));
        } else if (expression[index] == '(') {
            opStack.push('(');
            index++;
        } else if (expression[index] == ')') {
            while (!opStack.empty() && opStack.top() != '(') {
                char op = opStack.top();
                opStack.pop();
                Complex b = numStack.top();
                numStack.pop();
                Complex a = numStack.top();
                numStack.pop();
                numStack.push(Calculate(a, b, op));
            }
            opStack.pop(); // 弹出左括号
            index++;
        } else if (expression[index] == '+' || expression[index] == '-' || expression[index] == '*' || expression[index] == '/' || expression[index] == '^') {
            while (!opStack.empty() && Priority(opStack.top()) >= Priority(expression[index])) {
                char op = opStack.top();
                opStack.pop();
                Complex b = numStack.top();
                numStack.pop();
                Complex a = numStack.top();
                numStack.pop();
                numStack.push(Calculate(a, b, op));
            }
            opStack.push(expression[index]);
            index++;
        } else {
            index++; // 忽略空格和无效字符
        }
    }
    while (!opStack.empty()) {
        char op = opStack.top();
        opStack.pop();
        Complex b = numStack.top();
        numStack.pop();
        Complex a = numStack.top();
        numStack.pop();
        numStack.push(Calculate(a, b, op));
    }
    return numStack.top();
}

int main() {
    string expression = "3.5+222i -3 ^ 0.12 -2 5.1i arg * 33 4.667i abs 3 -4i cjg /";
    Complex result = Evaluate(expression);
    cout << result.real << " + " << result.imaginary << "i" << endl;
    return 0;
}