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:

Distribute:
 (−4−4i)⋅(−5−3i) = (−4)⋅(−5) + (−4)⋅(−3i) + (−4i)⋅(−5) + (−4i)⋅(−3i)

Simplify:
 20 + 12i + 20i + 12i²

Substitute i² with 1:
 20 + 12i + 20i + 12(1)

Combine real and imaginary terms:
 (20  12) + (12 + 20)i

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.