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:

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.

题目含义：求两个复数的乘法

思路：根据复数乘法公式  (a+bi)(c+di) = (ac-bd)+(ad+bc)i

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