(5i)(3i).jpeg "(-8i)(5i)(3i)")
Multiplying Complex Numbers: (-8i)(5i)(3i)
This article will guide you through the process of multiplying complex numbers, specifically focusing on the expression (-8i)(5i)(3i).
Understanding Complex Numbers
Complex numbers are numbers that can be expressed in 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
When multiplying complex numbers, we treat them like any other algebraic expression, remembering that i² = -1.
Steps:
- Distribute: Multiply each term in the first complex number by each term in the second complex number.
- Simplify: Combine like terms and remember that i² = -1.
Solving (-8i)(5i)(3i)
-
Step 1: Distribute (-8i)(5i)(3i) = (-8 * 5 * 3)(i * i * i) = -120i³
-
Step 2: Simplify -120i³ = -120 * (i² * i) = -120 * (-1 * i) = 120i
Conclusion
Therefore, (-8i)(5i)(3i) simplifies to 120i. This demonstrates the process of multiplying complex numbers and how to handle the imaginary unit 'i'.