# 537. Complex Number Multiplication

## 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

• 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);
}
}

• 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");
}
};

• 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'


• 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)
}

• 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;
}