(1+2i)(4+3i)

Jasonbradley

2 min read

·

Jun 16, 2024

12

Share

Multiplying Complex Numbers: (1 + 2i)(4 + 3i)

This article will walk you through the process of multiplying the complex numbers (1 + 2i) and (4 + 3i).

Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1 (i.e., i² = -1).

Multiplication Process

Multiplying complex numbers follows the distributive property, similar to multiplying binomials. Here's how to multiply (1 + 2i)(4 + 3i):

1. Expand using the distributive property: (1 + 2i)(4 + 3i) = 1(4 + 3i) + 2i(4 + 3i)

2. Distribute: = 4 + 3i + 8i + 6i²

3. Simplify using i² = -1: = 4 + 3i + 8i - 6

4. Combine real and imaginary terms: = (4 - 6) + (3 + 8)i

5. Final Result: = -2 + 11i

Therefore, the product of (1 + 2i) and (4 + 3i) is -2 + 11i.

Conclusion

Multiplying complex numbers involves applying the distributive property and then simplifying using the definition of the imaginary unit i. The result is another complex number expressed in the form a + bi.