(−4−4i)⋅(−5−3i)

Jasonbradley

2 min read

·

Jun 17, 2024

15

Share

Multiplying Complex Numbers: (−4−4i)⋅(−5−3i)

This article will walk you through the process of multiplying two complex numbers: (−4−4i)⋅(−5−3i).

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 just like we do with real numbers:

1. Distribute:

   • (−4−4i)⋅(−5−3i) = (−4)⋅(−5) + (−4)⋅(−3i) + (−4i)⋅(−5) + (−4i)⋅(−3i)

2. Simplify:

   • 20 + 12i + 20i + 12i²

3. Substitute i² with -1:

   • 20 + 12i + 20i + 12(-1)

4. Combine real and imaginary terms:

   • (20 - 12) + (12 + 20)i

5. Final result:

   • 8 + 32i

Conclusion

Therefore, the product of (−4−4i)⋅(−5−3i) is 8 + 32i.

This example demonstrates the straightforward process of multiplying complex numbers using the distributive property and remembering that i² = -1.