Question

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.

Example 2:

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.

Note:

1. The input strings will not have extra blank.
2. The input strings will be given in the form of a+bi, where the integer a and b will both belong to the range of [-100, 100]. And the output should be also in this form.

Solution

class Solution {
 public:
  string complexNumberMultiply(string a, string b) {
    std::string res;
    int a1, a2, b1, b2, r1, r2;
    int len_a = a.size(), len_b = b.size();
    auto p1 = a.find_last_of("+"), p2 = b.find_last_of("+");
    a1 = stoi(a.substr(0, p1));
    b1 = stoi(b.substr(0, p2));

    a2 = stoi(a.substr(p1 + 1, len_a - p1 - 1));
    b2 = stoi(b.substr(p2 + 1, len_b - p2 - 1));

    r1 = a1 * b1 - a2 * b2;
    r2 = a1 * b2 + a2 * b1;
    res = to_string(r1) + "+" + to_string(r2) + "i";

    return res;
  }
};