Complex Number Multiplication Python Solution

lcpy gen -n 537   # by problem number
lcpy gen -s complex_number_multiply   # by problem name

Input: num1 = "1+1i", num2 = "1+1i"
Output: "0+2i"
Explanation: (1 + i) * (1 + i) = 1 + i^2 + 2 * i = 2i, and you need convert it to the form of 0+2i.

Input: num1 = "1+-1i", num2 = "1+-1i"
Output: "0+-2i"
Explanation: (1 - i) * (1 - i) = 1 + i^2 - 2 * i = -2i, and you need convert it to the form of 0+-2i.

class Solution:
    # Time: O(len(num1) + len(num2))
    # Space: O(1)
    def complex_number_multiply(self, num1: str, num2: str) -> str:
        a, b = self._parse(num1)
        c, d = self._parse(num2)
        return f"{a * c - b * d}+{a * d + b * c}i"

    def _parse(self, num: str) -> tuple[int, int]:
        real, imag = num[:-1].split("+")
        return int(real), int(imag)