Helene is finding the sum open paren 9 plus 10 i close paren plus open paren negative 8 plus 11 i close paren She rewrites the sum as open paren negative 8 plus 11 close paren times i plus open paren 9 plus 10 close paren times i Which statement explains the property of addition that she made an error in using?
Answer
A
Helene incorrectly used the associative property by changing the order of the two complex numbers.
B
Helene incorrectly used the commutative 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 parts and imaginary parts should be grouped separately: (9 + (−8)) + (10 + 11)i = 1 + 21i. Helene instead rewrites each real number as though it also had a factor of i, turning 9 + 10i into (9 + 10)i and −8 + 11i into (−8 + 11)i. That is an incorrect use of the distributive property; the real numbers do not have a factor of i.
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