Question 1 • Advanced Algebra: Concepts and Connections
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 identity property by combining the real number and the coefficient of the imaginary part.
B
Aiko incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part.
C
Aiko incorrectly used the associative property by changing the order of the two complex numbers.
D
Aiko incorrectly used the commutative property by changing the order of the two complex numbers.
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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