what is the value of the product $(3 - 2i)(3 + 2i)$?

$\bigcirc$ 5
$\bigcirc$ $9 + 4i$
$\bigcirc$ $9 - 4i$
$\bigcirc$ 13

Question

what is the value of the product $(3 - 2i)(3 + 2i)$?

$\bigcirc$ 5
$\bigcirc$ $9 + 4i$
$\bigcirc$ $9 - 4i$
$\bigcirc$ 13

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Complex Numbers", "Powers of i" ], "new_concepts": [ "Complex Number Multiplication" ], "current_concepts": [ "Complex Numbers", "Powers of i", "Complex Number Multiplication" ] } ## Apply the difference of squares formula $$ (3 - 2i)(3 + 2i) = 3^2 - (2i)^2 $$ ## Simplify the terms using the definition of i $$ \begin{aligned} 3^2 - (2i)^2 &= 9 - 4i^2 \ &= 9 - 4(-1) \ &= 9 + 4 \ &= 13 \end{aligned} $$

5

9 + 4i

9 - 4i

13

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

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QUESTION IMAGE

Question

Explanation:

Apply the difference of squares formula

Simplify the terms using the definition of i

Answer: