# Complex Number Multiplication Problem

## Description

LeetCode Problem 537.

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].
• i^2 == -1.

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

Example 1:

``````1
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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:

``````1
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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.

## Sample C++ Code

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class Solution {
public:
pair<int, int> parse(string num) {
int i = num.find('+');
double real = stoi(num.substr(0, i));
double imaginary = stoi(num.substr(i+1, num.size()-i-2));
pair<int, int> res(real, imaginary);
return res;
}

string complexNumberMultiply(string num1, string num2) {
pair<int, int> a = parse(num1), b = parse(num2);
int real_a = a.first, imag_a = a.second;
int real_b = b.first, imag_b = b.second;

return to_string(real_a * real_b - imag_a * imag_b) + '+' + to_string(real_a * imag_b  + real_b * imag_a)+'i' ;
}
};
``````