Final answer:
By multiplying the complex numbers (8 + 3i) and (3 + 5i) using the distributive property, we find that the product is 9 + 49i, which does not match any of the provided answer choices, suggesting there may be a typo.
Step-by-step explanation:
To multiply the complex numbers (8 + 3i)(3 + 5i), we use the distributive property (also known as the FOIL method in this context), multiplying each term in the first complex number by each term in the second complex number. The product of two complex numbers is given by:
- (a + bi)(c + di) = ac + adi + bci + bdi2
Applying this to (8 + 3i)(3 + 5i) yields:
- (8)(3) = 24
- (8)(5i) = 40i
- (3i)(3) = 9i
- (3i)(5i) = 15i2
Combining these results, we get:
Since i2 = -1, we can substitute 15i2 with -15, so the expression simplifies to:
We then combine like terms:
- 24 - 15 + (40i + 9i)
- 9 + 49i
The final result is 9 + 49i. However, this option is not listed in the choices provided by the student, indicating a possible typo in the question or answer choices.