## Multiplying Complex Numbers: (6 + 2i)(4 - 3i)

This article will guide you through multiplying complex numbers, specifically the product of (6 + 2i) and (4 - 3i).

### Understanding Complex Numbers

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

### The Multiplication Process

Multiplying complex numbers is similar to multiplying binomials. We use the distributive property (also known as FOIL method) to expand the expression:

(6 + 2i)(4 - 3i) = 6(4 - 3i) + 2i(4 - 3i)

Now, we distribute:

= 24 - 18i + 8i - 6i²

Remember that i² = -1. Substituting this:

= 24 - 18i + 8i + 6

Finally, combine the real and imaginary terms:

= **(24 + 6) + (-18 + 8)i**

= **30 - 10i**

### The Result

Therefore, the product of (6 + 2i) and (4 - 3i) is **30 - 10i**.

### Summary

Multiplying complex numbers involves applying the distributive property, substituting i² with -1, and combining like terms to arrive at a simplified complex number in the form **a + bi**.