Question

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?
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.

Answer 1

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

She treated (a + bi) as (a + b)i, which is not valid. Correctly combine like parts:
(4 + 5i) + (−3 + 7i) = (4 − 3) + (5 + 7)i = 1 + 12i.