Operations with Complex Numbers

Question 5 • 26/27 ALGEBRA II A

Aiko is finding the sum (4 + 5i) + (–3 + 7i). She rewrites the sum as (–3 + 7)i + (4 + 5)i. Which statement explains the error Aiko made by using a mathematical property incorrectly?

Answer

Aiko incorrectly used the commutative property by changing the order of the two complex numbers.

Aiko incorrectly used the associative property by changing the order of the two complex numbers.

Aiko incorrectly used the identity property by combining the real number and the coefficient of the imaginary part.

Aiko incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part.

Explanation

Aiko changed 4 + 5i into (4 + 5)i, and –3 + 7i into (–3 + 7)i. That incorrectly treats the real numbers 4 and –3 as coefficients of i; the distributive property does not justify that change. The correct sum combines real parts and imaginary parts separately: (4 – 3) + (5 + 7)i = 1 + 12i. The statement that she misused the distributive property is choice D.

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