Question

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

a. Which property of addition did Helene incorrectly use?
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 incorrectly applied the distributive property to the addition of complex numbers by improperly combining the real and imaginary parts, which led to an error in the addition process.

Step-by-step explanation:

To identify the error Helene made in adding the complex numbers (9 + 10i) and (-8 + 11i), we analyze the properties of addition she may have used. The correct way to add complex numbers is by adding their real parts and imaginary parts separately:

(9 + 10i) + (-8 + 11i) = (9 - 8) + (10i + 11i) = 1 + 21i.

However, Helene rewrote the sum as (-8 + 11)i + (9 + 10)i, which implies a use of the distributive property, incorrectly applying it to the addition of complex numbers. The distributive property typically connects addition and multiplication, not the addition of two sums, particularly when dealing with complex numbers.

Therefore, the correct statement is that:

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