Complex Number Multiplication

Problem Description

Given two complex numbers represented as strings in the form "real+imaginaryi", return a string representing their multiplication.

Key Insights

• A complex number can be expressed as a + bi, where a is the real part and b is the imaginary part.
• The multiplication of two complex numbers (a + bi) and (c + di) follows the formula: (a + bi) * (c + di) = (ac - bd) + (ad + bc)i.
• We need to correctly parse the input strings to extract the real and imaginary parts.
• The result must be formatted back into the "real+imaginaryi" string format.

Space and Time Complexity

Time Complexity: O(1) - The operations performed are constant time due to fixed input size. Space Complexity: O(1) - Only a fixed amount of space is used for variables, regardless of input size.

Solution

To solve this problem, we will:

1. Parse the input strings to extract the real and imaginary parts of the complex numbers.
2. Use the multiplication formula for complex numbers to compute the resulting real and imaginary parts.
3. Format the result back into the required string format.

We will utilize basic string manipulation to extract the components and perform arithmetic operations to calculate the result.

Code Solutions