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Donte simplified the expression below.

4(1 + 3i) – (8 – 5i) = –4 + 8i

What mistake did Donte make?
A.He did not apply the distributive property correctly for 4(1 + 3i).
B.He did not distribute the subtraction sign correctly for 8 – 5i.
C.He added the real number and coefficient of i in 4(1 + 3i).
D.He added the two complex numbers instead of subtracted.

Respuesta :

JonHenderson55
The answer is: [A]: He did not apply the distributive property correctly for                                        4(1 + 3i) .
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Explanation:
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Note the distributive property of multiplication:
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a*(b+c) = ab + ac.
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As such: 4*(1 + 3i) = (4*1) + (4*3i) = 4 + 12i ;
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Instead, Donte somehow incorrectly calculated:
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4*(1 + 3i) = (4*1) + 3i = 4 + 31; (and did the rest of the problem correctly);

Note:  - (8 - 5i) = -8 + 5i (done correctly; 
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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:
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4+ 3i - 8 + 5i = -4 + 8i (the incorrect answer as stated in our original problem.
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This corresponds to: "Answer choice: [A]: He did not apply the distributive property correctly for 4(1 + 3i)."
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metchelle
Based on the given solution above made by Donte, the mistake that he made is that he 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:
4(1 + 3i) – (8 – 5i) 
4+12i - 8 + 5i
17i-4
so, 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!

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