0537. Complex Number Multiplication

537. Complex Number Multiplication

Topics

• Math
• String

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 (Java)

public String complexNumberMultiply(String a, String b) {
        StringBuilder sb = new StringBuilder();
        String[] tokenA = a.split("\\+|i");
        String[] tokenB = b.split("\\+|i");
        int realA = Integer.parseInt(tokenA[0]);
        int realB = Integer.parseInt(tokenB[0]);
        int imgA = Integer.parseInt(tokenA[1]);
        int imgB = Integer.parseInt(tokenB[1]);
        int real = realA * realB - imgA * imgB;
        int complex = realA * imgB + imgA * realB;
        sb.append(real).append("+").append(complex).append("i");
        return sb.toString();
    }