## Multiplying Imaginary Numbers: (5i)(3i)

This article will explain how to multiply the imaginary numbers (5i) and (3i).

### Understanding Imaginary Numbers

The imaginary unit, denoted by **i**, is defined as the square root of -1. This means that **i² = -1**.

### Multiplying (5i)(3i)

**Combine the coefficients:**Multiply the coefficients of the imaginary numbers: 5 * 3 = 15.**Multiply the imaginary units:**Multiply the 'i' terms: i * i = i².**Simplify using i² = -1:**Since i² = -1, we can replace i² with -1.

Therefore, (5i)(3i) = 15i² = 15 * (-1) = **-15**.

### Key Takeaways

- Imaginary numbers are numbers that can be written in the form
**bi**, where 'b' is a real number and 'i' is the imaginary unit. - When multiplying imaginary numbers, treat 'i' as a variable.
- Remember that
**i² = -1**.

By understanding these concepts, you can confidently multiply imaginary numbers and simplify expressions involving them.