(8-6i)(-4-4i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (8-6i)(-4-4i)

This article will demonstrate how to multiply two complex numbers: (8-6i) and (-4-4i).

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).

Multiplication Process

To multiply complex numbers, we use the distributive property (also known as FOIL method) like we do with binomials. Here's the breakdown:

1. Distribute: Multiply each term in the first complex number by each term in the second complex number. (8 - 6i)(-4 - 4i) = (8)(-4) + (8)(-4i) + (-6i)(-4) + (-6i)(-4i)

2. Simplify: Perform the multiplications and combine like terms. = -32 - 32i + 24i + 24i²

3. Substitute i² = -1: Replace any occurrences of i² with -1. = -32 - 32i + 24i + 24(-1)

4. Combine Real and Imaginary Parts: Group the real terms and the imaginary terms. = (-32 - 24) + (-32 + 24)i

5. Final Result: Simplify the expression. = -56 - 8i

Conclusion

Therefore, the product of (8-6i) and (-4-4i) is -56 - 8i.