(4-i)(6-6i)

Jasonbradley

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Jun 16, 2024

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

This article will explore the process of multiplying the complex numbers (4 - i) and (6 - 6i). We'll delve into the steps involved and the resulting complex number.

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.

Multiplication Process

To multiply two complex numbers, we use the distributive property, similar to multiplying binomials in algebra:

1. Expand the brackets: (4 - i)(6 - 6i) = 4(6 - 6i) - i(6 - 6i)

2. Distribute: = 24 - 24i - 6i + 6i²

3. Simplify: = 24 - 30i + 6i²

4. Substitute i² with -1: = 24 - 30i + 6(-1)

5. Combine real and imaginary terms: = (24 - 6) + (-30)i

6. Final Result: = 18 - 30i

Therefore, the product of (4 - i) and (6 - 6i) is 18 - 30i.

Conclusion

Multiplying complex numbers involves a straightforward process similar to multiplying binomials, with the key difference being the substitution of i² with -1. This results in a complex number expressed in the standard form of a + bi, where 'a' and 'b' are real numbers.