Based on the given solution above made by Donte, the mistake that he made is that h<span>e did not apply the distributive property correctly for 4(1 + 3i). The answer is option A. Here is why. If we simplify this, it would look like this: </span><span>4(1 + 3i) – (8 – 5i) 4+12i - 8 + 5i 17i-4 so, </span>4(1 + 3i) – (8 – 5i) should be equal to 17i - 4. Hope this is the answer that you are looking for. Have a great day!
The answer is: [A]: He did not apply the distributive property correctly for 4(1 + 3i) . _____________________________________________ Explanation: ______________________ Note the distributive property of multiplication: _____________________________ a*(b+c) = ab + ac. ____________________________ As such: 4*(1 + 3i) = (4*1) + (4*3i) = 4 + 12i ; _____________________________________ Instead, Donte somehow incorrectly calculated: _____________________________________ 4*(1 + 3i) = (4*1) + 3i = 4 + 31; (and did the rest of the problem correctly);
Note: - (8 - 5i) = -8 + 5i (done correctly; ___________________________________ So if Donte did not apply the distributive property correctly for 4*(1+3i)—and incorrect got 4 + 3i (as mentioned above); but did the rest of the problem correctly, he would have got: _____________________________ 4+ 3i - 8 + 5i = -4 + 8i (the incorrect answer as stated in our original problem. __________________ This corresponds to: "Answer choice: [A]: <span>He did not apply the distributive property correctly for 4(1 + 3i)." ___________________________</span>
