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?

Answer 1

Answer:

Step-by-step explanation:

Given that Helene is finding the sum (9 + 10i) + (–8 + 11i).

Also given that She rewrites the sum as (–8 + 11)i + (9 + 10)i.

The mistake she did is in the second term distributing i.

(9+10i) is not equal to (9+10)i

Similarly (-8+11i) is not equal to (-8+11)i

The correct method she should have done is

grouping real terms together and imaginary terms together and finding the sum

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

She made a mistake of taking out i from real term without changing the real term appropriately.

Thus she did the mistake of grouping unlike terms and factorising.

Answer 2

The answer is that Helene incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part.