which expression is equivalent to $(4 + 7i)(3 + 4i)$?

$\bigcirc$ $-16 + 37i$
$\bigcirc$ $12 - 28i$
$\bigcirc$ $16 - 37i$
$\bigcirc$ $37 + 16i$

Question

which expression is equivalent to $(4 + 7i)(3 + 4i)$?

$\bigcirc$ $-16 + 37i$
$\bigcirc$ $12 - 28i$
$\bigcirc$ $16 - 37i$
$\bigcirc$ $37 + 16i$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Complex Number Operations" ], "new_concepts": [], "current_concepts": [ "Complex Number Operations" ] } ## Expand the product of the binomials $$ (4 + 7i)(3 + 4i) = 4(3) + 4(4i) + 7i(3) + 7i(4i) $$ ## Simplify the individual terms $$ 12 + 16i + 21i + 28i^2 $$ ## Substitute $i^2 = -1$ and combine like terms $$ 12 + 37i + 28(-1) = 12 - 28 + 37i = -16 + 37i $$

(A) $-16 + 37i$

(B) $12 - 28i$

(C) $16 - 37i$

(D) $37 + 16i$

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

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QUESTION IMAGE

Question

Explanation:

Expand the product of the binomials

Simplify the individual terms

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

Answer: