Complex Number Multiplication - Leetcode Solution

The Complex Number Multiplication problem on LeetCode requires us to multiply two complex numbers represented as strings.

Complex numbers are numbers that have a real part and an imaginary part. They are typically represented in the form a + bi, where a is the real part and b is the imaginary part.

To multiply two complex numbers, we first need to understand how to multiply imaginary numbers.

To multiply two imaginary numbers i1 and i2, we use the following rule: i1 * i2 = -1 * (i1i2)

Where i1i2 represents the product of the magnitudes of i1 and i2, and the negative sign is introduced because i^2 = -1.

Now, let's move on to solving the problem. The input to the problem is two strings representing complex numbers.

For example, let's say the input is "1+2i" and "3+4i". Our first step is to extract the real and imaginary parts of both numbers.

Number 1: a1 = 1, b1 = 2 Number 2: a2 = 3, b2 = 4

Now, we use the formula for multiplying two complex numbers: (a1 + b1i) * (a2 + b2i) = (a1a2 - b1b2) + (a1b2 + a2b1)i

Substituting the values, we get:

(1+2i) * (3+4i) = (13 - 24) + (14 + 32)i = (-5 + 10i)

Therefore, the output for the given input is "-5+10i".

We can implement this solution in Python as follows:

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

Here, we first remove the "i" character from the input strings and split them based on the "+" sign. This gives us the real and imaginary parts of the complex numbers. We then use the formula to multiply the complex numbers and return the result as a string.

1