select the correct answer.

what is the value of the expression given below?
$8 - 3i) - (8 - 3i)(8 + 8i)\

\(\bigcirc$ $-80 + 43i$

$\bigcirc$ $-96 - 37i$

$\bigcirc$ $-80 - 43i$

$\bigcirc$ $-96 + 37i$

Question

select the correct answer.

what is the value of the expression given below?
$8 - 3i) - (8 - 3i)(8 + 8i)\

\(\bigcirc$ $-80 + 43i$

$\bigcirc$ $-96 - 37i$

$\bigcirc$ $-80 - 43i$

$\bigcirc$ $-96 + 37i$

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 of the complex numbers $$ \begin{aligned} (8 - 3i)(8 + 8i) &= 8(8) + 8(8i) - 3i(8) - 3i(8i) \ &= 64 + 64i - 24i - 24i^2 \ &= 64 + 40i - 24(-1) \ &= 64 + 40i + 24 \ &= 88 + 40i \end{aligned} $$ ## Subtract the product from the first term $$ \begin{aligned} (8 - 3i) - (88 + 40i) &= 8 - 3i - 88 - 40i \ &= (8 - 88) + (-3i - 40i) \ &= -80 - 43i \end{aligned} $$

-80 + 43i

-96 - 37i

-80 - 43i

-96 + 37i

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

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QUESTION IMAGE

Question

Explanation:

Expand the product of the complex numbers

Subtract the product from the first term

Answer: