(3i)(4i).jpeg "(2i)(3i)(4i)")
Multiplying Imaginary Numbers: (2i)(3i)(4i)
This article explores the multiplication of imaginary numbers, focusing on the expression (2i)(3i)(4i). We'll break down the steps and explain the key concepts involved.
Understanding Imaginary Numbers
The imaginary unit, denoted by i, is defined as the square root of -1. This means that i² = -1. Imaginary 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.
Multiplying Imaginary Numbers
When multiplying imaginary numbers, we treat i like any other variable, but we must remember that i² = -1.
Step 1: Multiply the coefficients
In our example, (2i)(3i)(4i), we multiply the coefficients: 2 * 3 * 4 = 24.
Step 2: Multiply the imaginary units
We multiply the i terms: i * i * i = i³.
Step 3: Simplify the result
Recall that i² = -1. We can rewrite i³ as i² * i. Substituting i² with -1, we get:
i³ = -1 * i = -i.
Step 4: Combine the results
Combining the results from steps 1 and 3, we have:
(2i)(3i)(4i) = 24 * (-i) = -24i
Conclusion
Therefore, the product of (2i)(3i)(4i) is -24i. This example demonstrates how to multiply imaginary numbers by following the rules of multiplication and using the property that i² = -1.