Final answer:
To find the product of 4-i and 4+i, we can use the FOIL method: First, Outer, Inner, Last. Applying this method, we get a product of 17.
Step-by-step explanation:
To find the product of 4-i and 4+i, we can use the FOIL method. FOIL stands for First, Outer, Inner, Last and is a method used to multiply two binomials.
First: Multiply the first terms of each binomial: 4 * 4 = 16.
Outer: Multiply the two outer terms: 4 * i = 4i.
Inner: Multiply the two inner terms: -i * 4 = -4i.
Last: Multiply the last terms of each binomial: -i * i = -i^2 = -(-1) = 1.
Now, combine these results: 16 + 4i - 4i + 1 = 17.
Therefore, the product of 4-i and 4+i is 17, so the correct answer is D) 17.