Complex Number Multiplication问题及解法

问题描述：

Given two strings representing two complex numbers.

You need to return a string representing their multiplication. Note i2 = -1 according to the definition.

示例：

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.

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:
The input strings will not have extra blank.
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.

问题分析：

将每个负数的a和b提取出来，根据运算规则，计算出新的a和b。

过程详见代码：

class Solution {
public:
string complexNumberMultiply(string a, string b) {
int i = a.find("+");
int j = b.find("+");
int a1 = stoi(a.substr(0,i+1));
int b1 = stoi(a.substr(i + 1,a.length() - i - 1));

int a2 = stoi(b.substr(0, j + 1));
int b2 = stoi(b.substr(j + 1, b.length() - j - 1));

return to_string(a1*a2 - b1*b2) + "+" + to_string(a1*b2 + a2*b1) + "i";
}
};