(−4−5i)⋅(1−i)

Jasonbradley

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Jun 17, 2024

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Multiplying Complex Numbers: A Step-by-Step Guide

This article will guide you through the process of multiplying the complex numbers (−4−5i) and (1−i).

Understanding Complex Numbers

Complex numbers are numbers of the form a + bi, where a and b are real numbers, and i is the imaginary unit, where i² = -1.

The Multiplication Process

To multiply complex numbers, we use the distributive property, similar to multiplying binomials.

1. Expand the product:

   (-4 - 5i) * (1 - i) = (-4 * 1) + (-4 * -i) + (-5i * 1) + (-5i * -i)

2. Simplify the terms:

   = -4 + 4i - 5i + 5i²

3. Substitute i² with -1:

   = -4 + 4i - 5i + 5(-1)

4. Combine real and imaginary terms:

   = (-4 - 5) + (4 - 5)i

5. Final Result:

   = -9 - i

Conclusion

Therefore, the product of (-4 - 5i) and (1 - i) is -9 - i. By following these steps, you can confidently multiply any two complex numbers. Remember to always substitute i² with -1 to obtain a simplified result.