Multiplying Complex Numbers: A StepbyStep 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.

Expand the product:
(4  5i) * (1  i) = (4 * 1) + (4 * i) + (5i * 1) + (5i * i)

Simplify the terms:
= 4 + 4i  5i + 5i²

Substitute i² with 1:
= 4 + 4i  5i + 5(1)

Combine real and imaginary terms:
= (4  5) + (4  5)i

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.