which equation shows an example of the associative property of addition?

$(-4 + i) + 4i = -4 + (i + 4i)$
$(-4 + i) + 4i = 4i + (-4i + i)$
$4i \cdot (-4i + i) = (4i - 4i) + (4i \cdot i)$
$(-4i + i) + 0 = (-4i + i)$

Question

which equation shows an example of the associative property of addition?

$(-4 + i) + 4i = -4 + (i + 4i)$
$(-4 + i) + 4i = 4i + (-4i + i)$
$4i \cdot (-4i + i) = (4i - 4i) + (4i \cdot i)$
$(-4i + i) + 0 = (-4i + i)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Associative Property of Addition" ], "current_concepts": [ "Associative Property of Addition", "Complex Number Properties" ] } ## Define the associative property of addition $$ (a + b) + c = a + (b + c) $$ ## Match the property to the given options $$ \begin{aligned} &\text{Option 1: } (-4 + i) + 4i = -4 + (i + 4i) \quad \text{(Matches } (a+b)+c = a+(b+c)\text{)} \ &\text{Option 2: } (-4 + i) + 4i = 4i + (-4i + i) \quad \text{(Incorrect terms/Commutative)} \ &\text{Option 3: } 4i \cdot (-4i + i) = (4i \cdot -4i) + (4i \cdot i) \quad \text{(Distributive)} \ &\text{Option 4: } (-4i + i) + 0 = (-4i + i) \quad \text{(Additive Identity)} \end{aligned} $$ ## Identify the correct equation $$ (-4 + i) + 4i = -4 + (i + 4i) $$

(A) $(-4 + i) + 4i = -4 + (i + 4i)$

(B) $(-4 + i) + 4i = 4i + (-4i + i)$

(C) $4i \cdot (-4i + i) = (4i \cdot -4i) + (4i \cdot i)$

(D) $(-4i + i) + 0 = (-4i + i)$

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

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QUESTION IMAGE

Question

Explanation:

Define the associative property of addition

Match the property to the given options

Identify the correct equation

Answer: