537.md

537 Complex Number Multiplication

Description

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.

Thinking Process

1. Easy approach, using high school math

Code

public class Solution {
    public String complexNumberMultiply(String a, String b) {
        StringBuilder sb = new StringBuilder();
        
        a = a.substring(0, a.length() - 1);
        b = b.substring(0, b.length() - 1);
        
        String[] first = a.split("\\+");
        String[] second = b.split("\\+");
        
        int real = 0;
        int complex = 0;
        
        real = Integer.parseInt(first[0]) *Integer.parseInt(second[0]) - Integer.parseInt(first[1]) * Integer.parseInt(second[1]);
        complex = Integer.parseInt(first[0]) *Integer.parseInt(second[1]) + Integer.parseInt(first[1]) * Integer.parseInt(second[0]);
        
        sb.append(real).append("+").append(complex).append("i");
        
        return sb.toString();
    }
}