10
QuizMultiple Choice

Distance and Midpoints in the Complex Plane

Question 10 • *PGHS Precalculus B

Helene is finding the sum (9 + 10i) + (–8 + 11i). She rewrites the sum as (–8 + 11)i + (9 + 10)i. Which statement explains the property of addition that she made an error in using?

Answer
A
Helene incorrectly used the commutative property by changing the order of the two complex numbers.
B
Helene incorrectly used the associative property by changing the order of the two complex numbers.
C
Helene incorrectly used the identity property by combining the real number and the coefficient of the imaginary part.
D
Helene incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part.

Explanation

The real part and the imaginary part must stay separate: 9 + 10i cannot be rewritten as (9 + 10)i, because distributing i would give 9i + 10i², not 9 + 10i. The same error occurs with −8 + 11i. So Helene incorrectly used the distributive property by combining the real number with the coefficient of the imaginary part; the correct choice is D.

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