Complex Number Multiplication — LeetCode 537 Python Solution

The problem

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].

Example

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.

Python solution

class Solution:
    def complexNumberMultiply(self, num1: str, num2: str) -> str:
        a1, b1 = map(int, num1[:-1].split("+"))
        a2, b2 = map(int, num2[:-1].split("+"))
        return f"{a1 * a2 - b1 * b2}+{a1 * b2 + a2 * b1}i"

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 537. Complex Number Multiplication is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

Related problems