Leet Code Problem #537. Complex Number Multiplication

Given two strings representing two complex numbers.
You need to return a string representing their multiplication. Note i² = -1 according to the definition.
Example 1:

Input: "1+1i", "1+1i"
Output: "0+2i"
Explanation: (1 + i) * (1 + i) = 1 + i2 + 2 * i = 2i, 

and you need convert it to the form of 0+2i.

Solution in C++:

    string complexNumberMultiply(string a, string b) {

        int a1 = 0;
        int a2 = 0;
        int b1 = 0;
        int b2 = 0;
        string ret;
        cal(a, a1, a2);
        cal(b, b1, b2);
        int real = a1 * b1 - a2 * b2;
        int imag = a1 * b2 + a2 * b1;
        char final_arr[30];
       
        sprintf(final_arr, "%d+%di", real, imag);

        for(int it = 0; it  < strlen(final_arr); ++it){
            ret.push_back(final_arr[it]);
        }
        return ret;
    }
   
    void cal(string s, int &a1, int &a2){
        int iter = 0;
        bool  is_a1_neg = false;
        char a[5] = {0};
        if(s[0] == '-'){
            is_a1_neg = true;
        }
        while(iter < s.length()){
           
            if(s[iter] == '+'){
               
                if(is_a1_neg){
                    s.copy(a, iter - 1, 1);
                    a[iter - 1] = '\0';
                    a1 = -atoi(a);
                } else {
                    s.copy(a, iter, 0);
                    a[iter] = '\0';
                    a1 = atoi(a);
                }  
                break;
            }
            ++iter;
        }
        ++iter;
        if(s[iter] == '-'){
            ++iter;
            s.copy(a, s.length() - iter, iter);
            a[s.length() - iter] = '\0';
            a2 = -atoi(a);
        } else {
            s.copy(a, s.length() - iter, iter);
            a[iter] = '\0';
            a2 = atoi(a);
        }
    }