Final answer:
The product of the complex numbers (8 + 5i) and (-7 + 9i) is found using the FOIL method, resulting in a final product of -101 - 107i.
Step-by-step explanation:
To find the product of the complex numbers (8 + 5i) and (-7 + 9i), we use the distributive property (also known as the FOIL method in this context) to multiply the two binomials:
(8 + 5i)(-7 + 9i) = 8*(-7) + 8*(9i) + 5i*(-7) + 5i*(9i)
This simplifies to:
-56 - 72i - 35i + 45i2
Since i2 = -1:
-56 - 72i - 35i - 45
Combine like terms:
-56 - 45 - (72i + 35i)
-101 - 107i
The final product of these complex numbers is -101 - 107i.