which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression $(-1 + i) + (21 + 5i)$?

$(-1 + i) + (21 + 5i) + 0$
$-1 + (i + 21) + 5i$
$(-1 + 21) + (i + 5i)$
$-(1 - i) + (21 + 5i)$

Question

which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression $(-1 + i) + (21 + 5i)$?

$(-1 + i) + (21 + 5i) + 0$
$-1 + (i + 21) + 5i$
$(-1 + 21) + (i + 5i)$
$-(1 - i) + (21 + 5i)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Commutative Property of Addition" ], "new_concepts": [], "current_concepts": [ "Commutative Property of Addition", "Complex Number Addition" ] } ## Identify the properties applied in each option $$ \begin{aligned} &\text{Original expression: } (-1 + i) + (21 + 5i)\ &\text{Option 1: } (-1 + i) + (21 + 5i) + 0 \quad \text{(Additive Identity Property)}\ &\text{Option 2: } -1 + (i + 21) + 5i \quad \text{(Associative Property of Addition)}\ &\text{Option 3: } (-1 + 21) + (i + 5i) \quad \text{(Commutative Property of Addition to reorder terms: } i + 21 = 21 + i\text{)}\ &\text{Option 4: } -(1 - i) + (21 + 5i) \quad \text{(Distributive Property / Factoring out } -1\text{)} \end{aligned} $$ ## Select the correct option $$ (-1 + 21) + (i + 5i) $$

(A) $(-1 + i) + (21 + 5i) + 0$

(B) $-1 + (i + 21) + 5i$

(C) $(-1 + 21) + (i + 5i)$

(D) $-(1 - i) + (21 + 5i)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Commutative Property of Addition" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the properties applied in each option

Select the correct option

Answer: