(3i)(−2i)(5i)

Jasonbradley

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Jun 16, 2024

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Multiplying Imaginary Numbers: (3i)(-2i)(5i)

This article will walk you through the process of multiplying the imaginary numbers (3i)(-2i)(5i).

Understanding Imaginary Numbers

Imaginary numbers are represented by the symbol i, where i² = -1. This property is crucial for understanding how imaginary numbers multiply.

Multiplying the Expressions

Let's break down the multiplication step by step:

1. (3i)(-2i):

   • Multiply the coefficients: 3 * -2 = -6
   • Multiply the imaginary units: i * i = i²
   • Substitute i² with -1: -6 * (-1) = 6

2. (6)(5i):

   • Multiply the coefficient: 6 * 5 = 30
   • Multiply by the imaginary unit: 30 * i = 30i

The Final Answer

Therefore, the product of (3i)(-2i)(5i) is 30i.

Key Takeaway

Remember the fundamental rule i² = -1 when multiplying imaginary numbers. This rule allows you to simplify expressions and obtain a final result in the form of a real or imaginary number.