(4i)(-3i)

Jasonbradley

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Jun 16, 2024

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Multiplying Imaginary Numbers: (4i)(-3i)

This article explores the multiplication of two imaginary numbers: (4i)(-3i).

Understanding Imaginary Numbers

Imaginary numbers are a fundamental concept in mathematics, denoted by the symbol 'i'. They are defined as the square root of -1: i = √-1. This means that i² = -1.

Multiplying the Imaginary Numbers

To multiply (4i)(-3i), we simply follow the rules of multiplication:

1. Multiply the coefficients: 4 * -3 = -12
2. Multiply the imaginary units: i * i = i²

This gives us: (4i)(-3i) = -12i²

3. Substitute i² with -1: -12 * (-1) = 12

Therefore, (4i)(-3i) = 12.

Key Points to Remember

• The product of two imaginary numbers is a real number.
• The key to solving this problem is understanding that i² = -1.
• You can always use the distributive property when multiplying expressions involving imaginary numbers.

By following these steps, we can efficiently multiply any two imaginary numbers and arrive at a simple, real-number solution.