README_EN.md

537. Complex Number Multiplication

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Description

A complex number can be represented as a string on the form "real+imaginaryi" where:

• real is the real part and is an integer in the range [-100, 100].
• imaginary is the imaginary part and is an integer in the range [-100, 100].
• i2 == -1.

Given two complex numbers num1 and num2 as strings, return a string of the complex number that represents their multiplications.

 

Example 1:

Input: num1 = "1+1i", num2 = "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: num1 = "1+-1i", num2 = "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.

 

Constraints:

• num1 and num2 are valid complex numbers.

Solutions

(a+bi)(c+di) = ac-bd+(ad+cb)i

Python3

class Solution:
    def complexNumberMultiply(self, num1: str, num2: str) -> str:
        a, b = map(int, num1[:-1].split('+'))
        c, d = map(int, num2[:-1].split('+'))
        return f'{a * c - b * d}+{a * d + c * b}i'

Java

class Solution {
    public String complexNumberMultiply(String num1, String num2) {
        String[] c1 = num1.split("\\+|i");
        String[] c2 = num2.split("\\+|i");
        int a = Integer.parseInt(c1[0]);
        int b = Integer.parseInt(c1[1]);
        int c = Integer.parseInt(c2[0]);
        int d = Integer.parseInt(c2[1]);
        return String.format("%d+%di", a * c - b * d, a * d + c * b);
    }
}

TypeScript

function complexNumberMultiply(num1: string, num2: string): string {
    let arr1 = num1.split('+'),
        arr2 = num2.split('+');
    let r1 = Number(arr1[0]),
        r2 = Number(arr2[0]);
    let v1 = Number(arr1[1].substring(0, arr1[1].length - 1)),
        v2 = Number(arr2[1].substring(0, arr2[1].length - 1));
    let ansR = r1 * r2 - v1 * v2;
    let ansV = r1 * v2 + r2 * v1;
    return `${ansR}+${ansV}i`;
}

C++

class Solution {
public:
    string complexNumberMultiply(string num1, string num2) {
        int a, b, c, d;
        sscanf(num1.c_str(), "%d+%di", &a, &b);
        sscanf(num2.c_str(), "%d+%di", &c, &d);
        return string(to_string(a * c - b * d) + "+" + to_string(a * d + c * b) + "i");
    }
};

Go

func complexNumberMultiply(num1, num2 string) string {
	parse := func(num string) (a, b int) {
		i := strings.IndexByte(num, '+')
		a, _ = strconv.Atoi(num[:i])
		b, _ = strconv.Atoi(num[i+1 : len(num)-1])
		return
	}
	a, b := parse(num1)
	c, d := parse(num2)
	return fmt.Sprintf("%d+%di", a*c-b*d, a*d+b*c)
}

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