(-3i).jpeg "(-5i)(-3i)")
Multiplying Imaginary Numbers: (-5i)(-3i)
This article will explore the multiplication of two imaginary numbers: (-5i)(-3i).
Understanding Imaginary Numbers
Imaginary numbers are a type of complex number that are defined as the square root of -1, denoted by the symbol i. This means that i² = -1.
Multiplying Complex Numbers
To multiply complex numbers, we use the distributive property just like we do with real numbers. We multiply each term in the first complex number by each term in the second complex number.
Solving (-5i)(-3i)
- Distribute: (-5i)(-3i) = (-5i) * (-3i)
- Multiply: (-5i) * (-3i) = 15i²
- Substitute: Since i² = -1, we can substitute: 15i² = 15(-1)
- Simplify: 15(-1) = -15
Therefore, (-5i)(-3i) = -15.
Conclusion
Multiplying imaginary numbers involves using the distributive property and the fact that i² = -1. By following these steps, we can simplify complex expressions involving imaginary numbers.