Aiko is finding the sum open paren 4 plus 5 i close paren plus open paren negative 3 plus 7 i close paren She rewrites the sum as open paren negative 3 plus 7 close paren times i plus open paren 4 plus 5 close paren times i Which statement explains the error Aiko made by using a mathematical property incorrectly?
Answer
A
Aiko incorrectly used the commutative property by changing the order of the two complex numbers.
B
Aiko incorrectly used the associative property by changing the order of the two complex numbers.
C
Aiko incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part.
D
Aiko incorrectly used the identity property by combining the real number and the coefficient of the imaginary part.
Explanation
To add complex numbers, combine the real parts and the coefficients of i separately: (4 + (−3)) + (5 + 7)i = 1 + 12i. Aiko’s rewrite turns the real numbers 4 and −3 into terms multiplied by i, as though they were coefficients of i. That incorrectly applies the distributive property; the real parts cannot be combined with the imaginary coefficients this way.
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