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

This article will explore the multiplication of the complex numbers (6 + 3i) and (6 - 3i). We'll use the distributive property and the fact that **i² = -1** to simplify the expression and arrive at a real number result.

### Understanding the Problem

We have two complex numbers:

**(6 + 3i)**: This is in the form of (a + bi), where 'a' and 'b' are real numbers, and 'i' is the imaginary unit.**(6 - 3i)**: This is the complex conjugate of (6 + 3i).

The product of a complex number and its conjugate always results in a real number.

### Solution

Let's multiply the complex numbers using the distributive property (FOIL method):

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

Expanding the expression:

= 36 - 18i + 18i - 9i²

Since i² = -1:

= 36 - 9(-1)

= 36 + 9

= **45**

### Conclusion

Therefore, the product of (6 + 3i) and (6 - 3i) is **45**. This result highlights the important property that the product of a complex number and its conjugate always yields a real number.