Question

Helene is finding the sum (9 + 10i) + (-8 + 11i). She rewrites the sum as (-8 + 11i) + (9 + 10i). Which statement explains the property of addition that she made an error in using?

A. Helene incorrectly used the commutative property by changing the order of the two complex numbers.
B. Helene incorrectly used the associative 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.

Answer 1

Helene correctly used the commutative property when she rewrote the sum of two complex numbers, as changing their order does not affect the result.

Step-by-step explanation:

Helene made no error in rewriting the sum as the commutative property of addition states that the order in which two numbers are added does not change the sum. That is, A + B = B + A. This property applies to real numbers, complex numbers, and even vectors. Therefore, when Helene rewrote the sum (9 + 10i) + (-8 + 11i) as (-8 + 11i) + (9 + 10i), she correctly used the commutative property, and her process was error-free.