(-6i)(3i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (-6i)(3i)

This article will guide you through the multiplication of two complex numbers, (-6i) and (3i).

Understanding Complex Numbers

Complex 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, defined as the square root of -1 (i² = -1).

Multiplying (-6i)(3i)

1. Direct Multiplication: We simply multiply the coefficients and the imaginary units: (-6i)(3i) = (-6 * 3)(i * i)

2. Simplifying: -6 * 3 = -18 i * i = i²

3. Substituting i² = -1: -18 * i² = -18 * (-1)

4. Final Result: -18 * (-1) = 18

Therefore, the product of (-6i) and (3i) is 18.

Key Points

• Remember that the imaginary unit 'i' is treated like any other variable during multiplication.
• When multiplying complex numbers, remember to substitute i² with -1 to simplify the result.
• The final answer, 18, is a real number, demonstrating that the product of two imaginary numbers can be a real number.