Formatted question description: https://leetcode.ca/all/537.html

# 537. Complex Number Multiplication (Medium)

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 1.

// OJ: https://leetcode.com/problems/complex-number-multiplication/

// Time: O(N)
// Space: O(N)
class Solution {
private:
vector<int> parse(string &s) {
vector<int> ans(2, 0);
ans = stoi(s);
int i = s.find_first_of("+");
ans = stoi(s.substr(i + 1));
return ans;
}
public:
string complexNumberMultiply(string a, string b) {
auto m = parse(a), n = parse(b);
int x = m * n - m * n, y = m * n + m * n;
}
};


Java

class Solution {
public String complexNumberMultiply(String a, String b) {
int aReal = Integer.parseInt(a.substring(0, a.indexOf('+')));
int aImag = Integer.parseInt(a.substring(a.indexOf('+') + 1, a.indexOf('i')));
int bReal = Integer.parseInt(b.substring(0, b.indexOf('+')));
int bImag = Integer.parseInt(b.substring(b.indexOf('+') + 1, b.indexOf('i')));
int mulReal = aReal * bReal - aImag * bImag;
int mulImag = aReal * bImag + bReal * aImag;
return mulReal + "+" + mulImag + "i";
}
}