## Simplifying Complex Numbers: (6i)(2i)

This article will guide you through simplifying the product of two complex numbers, specifically **(6i)(2i)**.

### Understanding Complex Numbers

Complex numbers are numbers that extend the real number system by including the imaginary unit **i**, where **i² = -1**. They are typically written in the form **a + bi**, where **a** and **b** are real numbers.

### Multiplying Complex Numbers

To multiply complex numbers, we treat them like binomials and use the distributive property:

**(a + bi)(c + di) = ac + adi + bci + bdi²**

Since **i² = -1**, we can substitute this value:

**(a + bi)(c + di) = ac + adi + bci - bd**

### Simplifying (6i)(2i)

Let's apply the above principles to our expression:

**(6i)(2i) = 12i²**

Now, substitute **i² = -1**:

**12i² = 12(-1) = -12**

Therefore, **(6i)(2i) = -12**.

### Conclusion

We successfully simplified the product of the two complex numbers, (6i)(2i), to a real number, -12. This demonstrates how complex numbers can interact and lead to real-valued results.