## Multiplying Complex Numbers: (8+2i)(8-2i)

This article will walk through the process of multiplying the complex numbers (8+2i) and (8-2i), and explain the significance of the result.

### 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.

### Multiplying Complex Numbers

To multiply complex numbers, we use the distributive property, just as we would with real numbers:

(8 + 2i)(8 - 2i) = 8(8 - 2i) + 2i(8 - 2i)

Expanding this expression gives us:

= 64 - 16i + 16i - 4i²

Since *i² = -1*, we can substitute to simplify:

= 64 - 4(-1)

= **64 + 4**

= **68**

### The Significance of the Result

Notice that the product of (8+2i) and (8-2i) is a **real number** (68). This is not a coincidence. The complex numbers (8+2i) and (8-2i) are **complex conjugates**.

**Complex conjugates** are pairs of complex numbers that have the same real part but opposite imaginary parts. When you multiply complex conjugates, the imaginary terms always cancel out, leaving only a real number.

### In Conclusion

Multiplying (8+2i) and (8-2i) results in 68. This demonstrates the concept of complex conjugates and how their multiplication always produces a real number.