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.

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:

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.

思路：
复数乘法公式：(a1+b1i)*(a2+b2i) = (a1a2 - b1b2) + (a1b2+a2b1) i

class Solution {
    public String complexNumberMultiply(String a, String b) {
        String[] A = a.split("\\+");  
        String[] B = b.split("\\+");  
        int a1 = Integer.parseInt(A[0]);  
        int b1 = Integer.parseInt(A[1].replace("i", ""));  
        int a2 = Integer.parseInt(B[0]);  
        int b2 = Integer.parseInt(B[1].replace("i", ""));  
        String res = (a1 * a2 - b1 * b2) + "+" + (a1 * b2 + a2 * b1) + "i";  
        return res;  
    }
}