(2i)(3i) Answer

Jasonbradley

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Jun 16, 2024

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

This article will explain how to multiply the imaginary numbers (2i) and (3i) and understand the concept behind it.

Understanding Imaginary Numbers

Imaginary numbers are represented by the symbol 'i' and are defined as the square root of -1. This means:

• i² = -1

Imaginary numbers are used in various areas of mathematics, particularly in complex numbers and solving equations.

Multiplying (2i)(3i)

To multiply (2i)(3i), we can follow these steps:

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

Therefore, (2i)(3i) = -6.

Key Points:

• Multiplication of Imaginary Numbers: When multiplying imaginary numbers, we multiply the coefficients and the imaginary units.
• i² = -1: Remember that the square of the imaginary unit 'i' is equal to -1.
• Result: The result of multiplying (2i)(3i) is a real number, -6.

Conclusion

Multiplying imaginary numbers can be simplified by understanding the definition of 'i' and remembering that i² = -1. The product of (2i)(3i) is -6, demonstrating how imaginary numbers interact with each other in mathematical operations.