select the correct answer.

what is the standard form of $(7 - 5i)(2 + 3i)$?

$\bigcirc -29 + 11i$
$\bigcirc -11 + 29i$
$\bigcirc 11 - 29i$
$\bigcirc 29 + 11i$

Question

select the correct answer.

what is the standard form of $(7 - 5i)(2 + 3i)$?

$\bigcirc -29 + 11i$
$\bigcirc -11 + 29i$
$\bigcirc 11 - 29i$
$\bigcirc 29 + 11i$

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 Arithmetic", "Distributive Property" ], "new_concepts": [], "current_concepts": [ "Complex Number Arithmetic", "Distributive Property" ] } ## Expand the product using the distributive property $$ (7 - 5i)(2 + 3i) = 7(2) + 7(3i) - 5i(2) - 5i(3i) $$ ## Simplify individual terms $$ \begin{aligned} 14 + 21i - 10i - 15i^2 \end{aligned} $$ ## Substitute $i^2 = -1$ and combine like terms $$ \begin{aligned} &14 + 11i - 15(-1) \ &= 14 + 11i + 15 \ &= 29 + 11i \end{aligned} $$

(A) $-29 + 11i$

(B) $-11 + 29i$

(C) $11 - 29i$

(D) $29 + 11i$

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

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QUESTION IMAGE

Question

Explanation:

Expand the product using the distributive property

Simplify individual terms

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

Answer: