(-2-i)(4+i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (-2 - i)(4 + i)

This article explores the process of multiplying two complex numbers, (-2 - i) and (4 + i).

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 (i.e., i² = -1).

Multiplication Process

To multiply complex numbers, we use the distributive property, just like we do with real numbers.

1. Distribute the first complex number: (-2 - i)(4 + i) = (-2)(4) + (-2)(i) + (-i)(4) + (-i)(i)

2. Simplify each term: = -8 - 2i - 4i - i²

3. Substitute i² with -1: = -8 - 2i - 4i - (-1)

4. Combine real and imaginary terms: = (-8 + 1) + (-2 - 4)i

5. Simplify: = -7 - 6i

Conclusion

Therefore, the product of (-2 - i) and (4 + i) is -7 - 6i. This result is also a complex number, illustrating that the product of two complex numbers is another complex number.