AnswersMO-Algebra II A-CRPerforming Operations with Complex NumbersQuestion 5
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Performing Operations with Complex Numbers

Question 5 • MO-Algebra II A-CR

Daine simplified the expression below. 8(1 + 2i) – (7 – 3i) = 1 + 5iWhat mistake did Daine make?

Answer
A
He did not apply the distributive property correctly for 8(1 + 2i).
B
He did not distribute the subtraction sign correctly for 7 – 3i.
C
He added the real number and coefficient of i in 8(1 + 2i).
D
He multiplied the two complex numbers when he should have subtracted.

Explanation

Distribute 8 to both terms: 8(1 + 2i) = 8 + 16i. Then subtracting (7 − 3i) gives 8 + 16i − 7 + 3i = 1 + 19i. Since Daine’s result has 5i instead of 19i, he did not correctly distribute the 8 across the parentheses.

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