(2-2i)(6-6i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (2-2i)(6-6i)

This article will guide you through multiplying the complex numbers (2-2i) and (6-6i). We'll use the distributive property (often referred to as FOIL) to simplify the expression.

Understanding Complex Numbers

A complex number is a number 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.

Multiplication using Distributive Property

1. Expand the expression: (2 - 2i)(6 - 6i) = 2(6 - 6i) - 2i(6 - 6i)

2. Apply the distributive property: = 12 - 12i - 12i + 12i²

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

4. Combine like terms: = 12 - 24i - 12

5. Simplify: = -24i

Conclusion

Therefore, the product of (2-2i) and (6-6i) is -24i.