(-6i)(3i) Simplify

Jasonbradley

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Jun 16, 2024

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Simplifying (-6i)(3i)

This article will guide you through the process of simplifying the expression (-6i)(3i).

Understanding Imaginary Numbers

Imaginary numbers are a fundamental concept in mathematics, often represented by the symbol 'i'. They are defined as the square root of -1, meaning i² = -1. This property plays a crucial role in simplifying expressions involving imaginary numbers.

Simplifying the Expression

1. Distribute: Begin by multiplying the coefficients and the imaginary units: (-6i)(3i) = (-6 * 3)(i * i) = -18i²

2. Substitute i²: Recall that i² = -1. Substitute this value into the expression: -18i² = -18 * (-1)

3. Simplify: Perform the final multiplication to get the simplified result: -18 * (-1) = 18

Therefore, the simplified form of (-6i)(3i) is 18.

Key Takeaways

• Imaginary numbers are defined by the property i² = -1.
• Simplifying expressions involving imaginary numbers often requires substituting i² with -1.
• Multiplication of complex numbers follows the distributive property.

By understanding these concepts, you can confidently simplify expressions involving imaginary numbers like (-6i)(3i).