which expression is equivalent to $(4 + 6i)^2$?

$\bigcirc$ $-20 + 48i$
$\bigcirc$ $8 + 12i$
$\bigcirc$ $16 - 36i$
$\bigcirc$ $20 + 48i$

Question

which expression is equivalent to $(4 + 6i)^2$?

$\bigcirc$ $-20 + 48i$
$\bigcirc$ $8 + 12i$
$\bigcirc$ $16 - 36i$
$\bigcirc$ $20 + 48i$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Complex Roots" ], "new_concepts": [ "Complex Number Operations", "Squaring Complex Numbers" ], "current_concepts": [ "Complex Roots", "Complex Number Operations", "Squaring Complex Numbers" ] } ## Expand the squared binomial $$ (4 + 6i)^2 = 4^2 + 2(4)(6i) + (6i)^2 $$ ## Simplify each term $$ 16 + 48i + 36i^2 $$ ## Substitute $i^2 = -1$ and combine like terms $$ 16 + 48i + 36(-1) = 16 - 36 + 48i = -20 + 48i $$

(A) $-20 + 48i$

(B) $8 + 12i$

(C) $16 - 36i$

(D) $20 + 48i$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Complex Number Operations" ] }

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Question

Explanation:

Expand the squared binomial

Simplify each term

Substitute \(i^2 = -1\) and combine like terms

Answer: